Urban savant is your best class option, but...
would leave me very short on Class Skills and Skillpoints though so I need to remedy that
I mean, just up front, you could simply not. For one thing, the best “remedy” even possibly available to you is only going to get you 4 skill points if you’re only taking one level and that level isn’t 1st, since at best you’re looking at 6+Int skill points instead of 2+Int. You would get more skill points by just taking Open Minded, or even better just not shuffling away the Nymph’s Kiss feat you are probably using to qualify for saint anyway. But more importantly, you have a ton of spells and spells trivially replace skills. Your skill rank requirements are fairly mild—the 6 ranks of Bluff for ur-priest are your greatest challenge, and that’s a class skill for sha’ir. All the rest are typical spellcaster-y skills (Concentrate, Knowledge (arcana/nature/religion/the planes), Spellcraft) with a lot of overlap. You really don’t “need to remedy” this.
Which is good, because all of your options here require 8 ranks in at least one skill. That means you’re gonna need a 9th-level bard with Song of the Heart to perform inspire greatness on you to give you 3 bonus HD, and then you need a 7th-level psion to manifest psychic reformation on you during the song so you can rearrange your 1st-level skill points to meet the requirements. Even then, you also need Favored and Primary Contact (Cityscape) to get a single bonus rank in a single skill to actually hit 8, since even with +3 HD your skill rank maximum is 7, not 8.
But if you do that, you are looking at potentially qualifying for urban savant (Cityscape). It actually requires the same Favored feat you needed for Primary Contact, which is good because you’ll also need Educated (Eberron Campaign Setting) since urban savant requires Knowledge skills that the sha’ir does not natively have in-class. That covers all your feats.
For class features, it requires “Bardic knowledge class ability (at DM's discretion, can be replaced by Knowledge (History) 2 ranks,” so that’s an open question. Considering everything else you expect the DM to allow, this seems like a done deal.
For skills, it needs 8 ranks in just one skill (and you even get a choice about which one), and 2 ranks in three others (including Knowledge (history) in place of bardic knowledge), for 14 total (so your sha’ir’s 20 skill points at 1st level is plenty).
Also, the 1st-level class features of urban savant are pretty good: in addition to 6+Int skill points and advancing your spellcasting, you get to cast all of your arcane spells in light armor, and you have a weird ability sort of like the archivist’s dark knowledge that allows you to ascertain the strengths of a variety of creatures.
I have checked every other prestige class that advances spellcasting and has 6+Int (or more) skill points per level, and all of them require more difficult things, or fail to advance spellcasting at 1st. You can cheese harder to get access to several of them, but urban savant also happens to be just about the best of them, at least if only taken for 1 level.