I can't find anything besides magic items that do what you want. Nothing else reaches the bar you've set. It doesn't even appear official or 2nd-party feats can let a factotum use guidance of the avatar [div] ("Spellbook" here). Consider adding the spell guidance of the avatar to your spell list so that employing wands of it are easier via 1 level of the cloistered cleric (UA 50) variant cleric; this gets decent skill points, and 3 Domains--or 2 Domains and, with the DM's permission, swap out the knowledge Domain (as per CC 52-3) to acquire the feat Knolwedge Devotion (CC 60) that way rather than spending your level-up feats.
These are listed in their possibility of approval. They start reasonable and get progressively more shady. Steel yourself for fights and recrimination if drawing from the bottom of the list. I am only presenting the information; the DM must determine if and how the following function in his game. Omitted are even more obvious sources of acquiring spellcasting (e.g. a minor ring of spell storing (DMG 233) (18,000 gp; 0 lbs.), an ioun stone (vibrant purple prism) (DMG 260) (36,000 gp; 0 lbs.))
- A wand of guidance of the avatar (2nd-level spell at caster level 3) (90 gp/charge; 0 lbs.). Consider a wand chamber (Du 30, 34) (100 gp; 0 lbs.) for your gnome quickrazor. Requires successful Use Magic Device skill checks. Requires only core (and a general splatbook for the wand chamber); the easiest way.
- A minor schema of guidance of the avatar (2,400 gp; 0 lbs.). You can learn more about minor schema, which are like 1/day scrolls, on MoE 122. Requires a setting-specific splatbook.
- A custom magic item, probably a helmet. Even a generous DM may say that an item capable of producing an effect like the spell guidance of the avatar at will is a bargain at 80,000 gp (it provides a +20 skill bonus, after all), especially for your character. The price might drop by pointing at the crystal ball with true seeing (DMG 253) (80,000 gp; 7 lbs.), which is far deadlier to campaigns than +20 to skill checks. Requires only core but needs DM approval.
- A spellworm (the 2nd-level Clr spell guidance of the avatar at caster level 3) (Dragon #343 80-1) (300 gp; 0 lbs.). The DM must house rule the spellworm (the description says that "casting the stored spell is a standard action" in one paragraph then in the next says that "the host casts the spell as a full-round action"--I'm not making that up). Essentially a potion without the potion's baggage, ingest many and more whenever you've a spare 300 gp--the power of spellworms apparently exists until expended. You'll have worms, though, and that's gross. Second-party material.
- A command word activated custom item of guidance of the avatar, probably a helmet. According to DMG 285 this has a base price of 2 (as a 2nd-level spell) x 3 (as a 3rd-level caster) x 1,800 gp (for a command word activated item) = 10,800 gp, and a market price of 21,600 gp. Requires only core but needs DM approval and is arguably underpriced.
- +1 Tiny spell storing (DMG 225) (+1 bonus) arrows (50) (8,300 gp 5 sp; 0.3 lbs.), each loaded with the spell guidance of the avatar, costing 60 gp per casting according to Spellcasting and Services (PH 129) for an extra 3,000 gp. Use them as improvised weapons to stab yourself and subsequently gain the spell's benefits. More expensive than a wand but avoids Use Magic Device skill checks. Whether the weapon special ability spell storing can be applied to ammunition is the subject of violent conflict. Broach this possibility only among good friends. Requires only core but needs DM approval.
- +1 spell storing fukimi-bari (3) (8,350 gp each; 1/10 lb. each) (AE 7) loaded with the spell guidance of the avatar, costing 60 gp per casting according to Spellcasting and Services. Attempt this only if your group accepts the previous. Put the 3 +1 spell storing fukimi-bari in your mouth, pause while other players crack wise, spit all 3 at yourself as an attack action, and gain the benefits of the spell guidance of the avatar thrice (not +60 but 3 separate activations). Requires an unupdated 3.0 splatbook and DM approval.
- A knowstone (guidance of the avatar) (Dragon #333 93) (4,000 gp; 0 lbs.). If the DM allows characters to employ the Use Magic Device skill to spend turn attempts they don't have to activate magic items (like Lidda does with the magic chalice on PH 86), he may allow characters to use spell slots they don't have to activate magic items. Not only does a knowstone "provide its bearer with knowledge of the inscribed spell" but also "he can then use his spell slots to cast [the inscribed spell] normally." Requires 2nd-party material and a potentially campaign-changing reading of the Use Magic Device skill.
- An automatically resetting boon trap (Du 136) of guidance of the avatar (approx. 3,120 gp) on your spell component pouch. Once per round as a free action that doesn't provoke attacks of opportunity trigger the trap by retrieving a spell component (I recommend a live spider (PH 283)). Requires a general splatbook but a host of DM interpretations, and the campaign implications of boon traps are stunningly far-reaching.
The Spell Itself
I can't imagine a class that wouldn't benefit from being able to use the 2nd-level Clr spell guidance of the avatar [div] ("Spellbook" here). However, it's author might have a different definition of what makes a balanced spell than other writers do. The only other spell contribution the author's made that I can find is the spell dirge of discord [ench] ("Spellbook" here), which in the link is a 5th-level Clr spell but was overhauled in Complete Adventurer on page 45 to a 3rd-level Brd spell (the updated version changes the original spell's ability to give affected creatures a -8 penalty to Dexterity to a more reasonable -4 penalty to Dexterity). Also, the spell guidance of the avatar is 3.0 material, making it suspect at some tables, and wasn't included, like many older published-first-on-Wizards-Web-site spells were, in the Spell Compendium. It's an orphan spell, existing solely on that page, a relic of a past edition, never officially referenced again. In short, don't marry it yet--even a reasonable DM might not allow the spell guidance of the avatar into his game.