I did a similar thing last year, but your high pressure/low volume tire inflator is not likely to be the best choice. The inflators designed for air mattresses, etc will be cheap and deliver higher volumes of air at lower pressures than the tire inflator. Tire pump is designed to deliver lower volume at higher pressures.
I also was specifically trying to cool a 30-06 derivative gun (270) so I took a random worthless case, cut the neck off, drilled the base out, adapted a 90 deg fitting to that. So I can close the bolt partially, holding the moded case in the chamber for a near perfect seal.
My $12 inflator from amazon may or may not last long, but it blows a ton of volume, can run with a 120v adaptor and also runs off my 12v jump starter lithium battery. Range where I shoot has 120v plugs, so no problem.
How loud is the Dewalt? My Milwaukee tire inflator is too loud. Of course, we have on ear protection, but its just annoying to have that darn thing running between shots when I want to take off my muffs -- precisely in the Summer when you need to cool a barrel.
