The reason it crashes with TinyXP is that TinyXP is missing components (files and/or services) required to use WiFi.
Yet another reason why I eschew those pre-made stripped down versions of Windoze.
You have two options:
1: Determine which files, serivces, registry keys are missing from TinyXP that prevent your Wifi from working properly and put them back.
2: Do a full install of XP and strip it down yourself.
Neither one is very appealing.