Yes I believe so, a bit like how they use ‘go to the bathroom’ a lot in the US, even if there is no actual restroom involved.

I would say this is common (euphemistic) usage in informal speech. Short for something like ちょっとトイレに行ってくる, etc.
I need to go to the bathroom, I need a p***, I need to p** etc.

It's important to remember that the character says トイレ while in the middle of the woods. So barring very specific settings, it's probable there isn't a proper bathroom at all. The person will have to go somewhere in the middle of the woods. bothトイレ and 手洗い are words you use when going to the bathroom, or washing your hands, and the like, but the latter is more likely to mean washroom.

Based on the context and the use of トイレ, I would choose this suggested translation and modify it based on the original context.