Even if you wash your hands in the toilet, you have to take it as a given that any door handle you touch in the toilet has just recontaminated you. Open cuts etc are a recipe for disaster. So I carry a bottle of alcohol based handwash in my bag and 2-3 medical grade steri-wipes in my on body kit. I take one out and have it ready BEFORE I enter the toilets.

If I'm not happy with the toilets (poorly maintained or I think that druggies are using them) and I have to use them then I use the medical grade disposable gloves I carry instead.

If I have to defecate then the toilet seat gets a steri-wipe or I use my blow-torch lighter on low to sterilise the surface.