I’m playing a 3.5 campaign starting at 3rd level in a desert city. I want to play a thief type character but don't enjoy all the skills of the rogue. Is there a non-magical class that has the thief skills (Open Lock, Sleight of Hand, Escape Artist, Bluff, and such) without the extra skills?
It's a real challenge to find base classes other than rogue which have the Open Lock skill in particular, and don't have spells. Nevertheless, a perusal of the Character Class Index reveals two strong candidates for your needs:
Ninja (Complete Adventurer)
A class similar to rogue, but with monk-like abilities.
Wilderness Rogue (Unearthed Arcana)
This variant from Unearthed Arcana loses the Appraise, Diplomacy, Decipher Script, Forgery, and Gather Information skills, while retaining Open Lock, Sleight of Hand, Escape Artist and Bluff. It also gains Handle Animal, Knowledge (geography), Knowledge (nature), Ride, and Survival as class skills. Useful in a desert city.
It also appears in the SRD under Variant Characters.
Factotum, from Dungeonscape, gets every skill ever in-class. That certainly includes everything you’re interested in. Factotum also does have some magic, but is not a primary spellcaster—instead, their whole schtick is “a little bit of everything.” They have trapfinding, they get lots of skill bonuses, they can cast a few arcane spells a day, they can turn undead as a low-level cleric, and at 19th level, they can straight-up steal other class’s class features (of 15th-level or lower) for a few minutes each day.
Literally anything—once you get the skill in-class despite your class
Also worth pointing out is the Able Learner feat from Races of Destiny. Able Learner allows you to buy cross-class skill ranks for only 1 skill point, rather than 2, which can go a long way towards making your thief out of any class. Your skill rank maximum would still be half what it should be, but you can fix that by getting the skill in-class for at least one level—that increases your maximum permanently. One of the more popular ways to use factotum, for example, is to take just one level and Able Learner, just to get the “all skills in-class” thing for whatever other classes they might want. You could do similarly with rogue or other classes that get the skills you need.
If it’s just one skill you’re after, human paragon from Unearthed Arcana can permanently make one skill a class skill. The class is really mediocre, though.
Finally, Aereni Focus from Eberron Campaign Setting and Flexible Mind from Dragon vol. 326 can make one or two skills in-class for you permanently, no dipping necessary. Then you can literally use whatever you like.