Generally, for a playthrough like that, stealth is a sure bet.
A bit of hacking won't hurt, either, because you can't hide from turrets and they'd better be on your side.
Unless you go the PSI/Unarmed route, which is hard by itself, you'll have to occasionally buy repair or health stuff, which I think is less traitorous to the idea than savescumming every single container.
If you spread your skills a little, you should find weapons and grenades enough to always have something on hand.