In particular, will I have serious difficulty if I compeletely neglect both Lockpicking and Trap Disarming?

(This means no thief and no putting explorer's skill points in those skills.)

You can carry additional lockpicks or bash down chests (it will take some food to recover) and you can heal through traps (or ignore them entirely with 100 in resists).

The only thing you will truly miss on is some very small amount of exp per disarmed trap and unlocked chest.

I really hate the "utility rogue" design present in so many games. Usually it doesn't add interesting gameplay. It just makes you choose between the nuisance of traps vs having to carry around a dead weight utility rogue all game. The only good thing about Thief is that if you level up Shuriken every single time, then you can rapidly stack tons of bleeding damage every time that it matters. It's a pretty fair trade - you only really have 5 fully-productive party members most of the time, but that #6 stacks a hilarious amount of DPS when you really need it. (If your enemy doesn't bleed, then that's another story... Maybe holy magic will pick up the slack.)