Answer: Unfortunately I am not an expert on moths. Based on your description it is difficult to take a guess. There is a photo of the moth stage of the squash vine borer at the following page, perhaps it is that as it does have some orange. You may need to cut and paste the complete url into your browser to make it work correctly.
You might be able to recognize it in an illustrated book of garden pests -- if it is a pest -- or possibly at the following butterfly web site. Take a look for example at the Northern Hairstrike and the Orange Tip White.
Or, you might find it listed at the following web site specifically on moths of New Jersey.
Generally speaking, the moths will not harm the plants but their larvae could. If you see caterpillars or worms on your plants, then you can treat with Bt, or you can handpick. Also keep a sharp eye out for signs of squash borers, or try covering your squash with a spun polyester fabric as a means of excluding the moths. (You will need to hand pollinate if you do this.)
Also, your county extension may be aware of specific pests that predominate in your area and can tell you approximately what week they usually appear locally. That might help you narrow things down as well.
I'm sorry I can't be more specific for you.
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