will give off some fumes when you first put some high heat on the stove. That is normal and the thing to realize is that will stop giving off fumes after it has reached some high temperatures over several cycles of being heated.
So the thing to do is paint
it, let it cure for a week or so. Turn on the stove, let it get good and hot, open the windows
and doors and let it fume. Do this step several times before you go camping.
You don't notice the fumes on items that have had enamels applied in a factory as they have already been cured in an oven at high temperatures so the fume generating part of the paint
cure was already done at the factory before you used the product.
So don't let the concept of the paint producing some fumes at the first few uses stop you from repainting the stove. It is not going to be a constant thing, it is just a temporary situation that is part of the paint cure. Expect it to happen, it is OK for it to happen, just ventilate and don't be inside the trailer while it is going on.
If you paint a woodstove or Bar-b-que or even a car engine it does the same thing of producing fumes while baking in the finish at first.
The only problem I have had with painting
a stove top is when using the color white. It yellowed over time in the areas around the burner where the temperature was the highest. So I would recommend a darker color if you want to avoid that yellowed look.