Getting water in the regulator or gas valve could ruin it, otherwise you'd just want to make sure it dries out completely before plugging it into power. A safe recommendation though would be this is not under normal circumstances a good idea. In this case though, it's kind of a why not because what are you going to do but throw it away anyhow.
Not sure how much luck you're going to have even doing this though. I was on a service call once at a lodge/resort in the mountains that wasn't open year around. In the off season mice had made a home in the oven and this same complaint was the result. The mice had actually gotten into the insulation inside the oven walls and even though the owner had cleaned the entire oven to a shine it still had that distinct oder when it began heating. The smell was just saturated into the insulation in the oven walls.
This was a $25,000.00 commercial oven, so the repair cost of me taking every aspect of the oven apart and replacing the insulation was justified in this case. For a residential oven though, you're likely going to find the expense in just even your own time isn't going to be worth doing this.
So you're likely going to end up trashing it no matter what, so no harm in just trying, but spraying it outside with the hose isn't going to get the smell out of the insulation in the oven walls which is the most likely strongest source of the problem.
If you try this, and find afterward you have ruined the gas valve or the regulator, I wouldn't waste your money buying these parts to only discover the smell is still there once you get it heating again.
Probably going to just want to look into getting a new or used oven and then a cat to solve the mouse problem. | 
