I'd recommend doing some testing and playing with alternate paints/coatings prior to diving in and hitting the entire ship. I can't, and never would, speak for others, but I've had issues with using the Rustoleum Chrome. The last time I used it was on a ST: DISCO phaser about 2-3 years ago. I'd used the same brand and color several times in the past and never noticed any issues (not the type I'm talking about), but I also hadn't used it on any parts that had been touched very much.
My daughter was the first to notice it right after she brushed her fingers across a couple of parts when she was looking it over for recommendations and version 2 improvements. After each touch or rub the chrome painted parts turned grey, almost tarnished. I pretty much shelved the project shortly after actually watching season 1... Anyway, I just checked it and the paint is still reacting to being touched. I didn't apply any coatings to the end model and don't recall what my plan was. If I were to guess, I would've added a coating of some kind, mainly because it would have been a handed prop.
Here're a few photos for your reference that show what I'm talking about... red arrowed surfaces have been touched or brushed and green arrowed surfaces are untouched. Maybe I didn't shake the can well enough, but I don't think so. Anyhow, just trying to help.
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