I just restarted MM7 without a Thief but with an Archer, as per the manual and google, Archers can get Expert Disarm even without any promotions....yet all 3 disarm trap expert "teachers" are telling me I must be Master Archer or Sniper to get the expert skill? Are the tables wrong or is there a glitch in the game?

Some quick online searching indicates the Archer should be able to get to Expert without a promotion.

Forgive me for such basic questions, but some things to verify:
1) Do you have the skill?
2) Do you have enough skill points in the skill?
3) Are you at the right skill hut?
4) "All 3 teachers"? Looks like there are only 2 teachers for expert Disarm Trap. Which skill trainers have you visited?

Because William Lasker the king of the thieves also offer expert in disarm and stealing those skills have 3 expert trainers.
The info you found on the website is wrong or you miss read but archer can't become expert in disarm until after their promotion. if you right click a skill for info anything in yellow requires you to have a promotion before you can use a trainer for that rank.

I seem to recall only one of those skills has three trainers, while Lasker is the second trainer for one of them. At least one site says Disarm has 3.

None of the sites I've scanned indicate that an Archer can't get to Expert Disarm, but they may have just been quoting the manual and the manual is wrong. *shrug*

You are using some wrong manual. Russian manual doesn't lie and says you need 2nd promotion for Archer to become Expert in Disarm Traps.

I do have the skill and 5 skill points on it (clearly not enough as everything outside of Harmondale is blowing up in my face) and about 12k gold. I went to the hut in the south of Tatalia, there's one in Tuleran Forest and one in the Erathian Sewers, all for expert, all say that I need the 2nd promotion.

I'm using the GOG manual that came with the game and it still has that little E next to Archer....so manual is incorrect?

That is correct, the manual is incorrect. You do need the second promotion. That is why when I play a good play through I always go with a thief. A monk will work for an evil play through. Expert is not enough for disarm trap and always need at least mastery.

And Perception will help keep down the damage.

Yes, but it isn't really reliable, and everyone that is going to avoid damage would have to invest valuable skill points (and most classes can't take it very high, iirc).

I never worried too much about disarm. My Knight had basic level (if it was a special chest, I kept around high level rings as aids that sometimes worked); my other players had expert perception; and I liked two Wizards in my Party so one could get Telekinesis ASAP (M&M7). Once in a while my Cleric got sucked dry healing after a blow-up. But using Telekinesis was always fun trying to figure out the angle, how far away, trying to get a doorway to take most of the explosion.
There is that one haunted house that everyone tackles early. I can't say how many times my knight was dragging three dead players to the temple. That house I wish I had Master level disarm.
Edit for clarity

And I'm always like "Thief, you're up!" and either *click* or *boom*. I dislike taking damage I don't feel that I need to take, and I likewise don't like spending spell points I don't feel I need to spend. That classic "I know it's the final boss, but I might NEED those elixirs later!"

It's Markham's treasure room that sends people off for me.