I'm currently playing Fallout 1 once more and decided to not pick up skills which I'm calling "standard set". Before I was always picking speech + two from small/big/energy weapons. Now I've decided to choose a prepared character - Natalia Dubrovhsky. She has Sneak, Steal and Unarmed as tag skills. I know Fallout 2 has many improvements for unarmed fight but Fallout 1 does not. But I can still use targeted attacks.
Is it possible to finish Fallout 1 with some diplomatic/thief character? What would be the best strategy for this?