Very interesting idea. You'd want to extract the hop flavor without the bitterness. I'd use a french press to do this, being careful not to heat the hops too long (the longer they are hot, the more isomerization of the hop oils, which increases the bitterness). I'd say 1 oz max, heat in french press for 2 or 3 minutes with 200F water, press, and (if using hop pellets) probably filter through a coffee filter to make sure none of the particles make it into the cheese. With leaf hops, this probably wouldn't be necessary.
I'd pick an American hop with a citrus aroma, but low in alpha acids (the measure of bitterness). The ubiquitous Cascade would be ideal I think.
The hop can't be in the cheese. It's a bitter weed. I've tried using them in salsa. No bueno.
I'd use them in a smoked cheese.
+1 for great advice. I'd say 5 minutes for aroma, 10-15 max for flavor, and out. Longer, and you risk isomerization and bitterness contribution, like pawn said.
Another thing you might try is something I used to do as a kind of dry-hopping routine, modified for forced CO2 bottling and kegging, as opposed to cask conditioning. Done with beer, it's simply a slurry created in beer that macerates for a couple days. I forget my ratios but also what pawn indicates, hops with great aromatic volatiles and low alpha and beta acids - he mentions cascade, I also like centennial for American ale styles, but prefer the goldings - East Kent, Styrian, along with WGV (stands fro Whitbread Golding Variety), First Gold (developed from WGV), for bitters, pales, India pales; and then Northdown, some others I've since forgotten (it's been close to 15 years since I was in brewing) for strong dark porters and stouts (fuggles was a workhorse in my strong dark ales, but more as an earthy & grassy/"fresh fields" backbone...not a huge fan of the hop as a standalone hop). Given the short maceration time, you load heavier than you normally would for a dry hopping routine, and you must use pellets.
Macerate the hops in a good bitter, say. It's important to really mix the slurry well, though try not to agitate the beer (introducing O2) so much as thoroughly mixing for several minutes. Macerate for 2-3 days, then crash cool and pull the cool beer off the top. You can filter, but more likely than not you should have a decent, clear solution to use as an aroma (mostly, with some minor flavor) agent - perhaps in a brine?
Not sure how well it would transfer to cheese, but I'd say it's worth a try. Depending on the cheese style, it would be fun to play with these American or British hops. Actually, the "noble" lager hops might be great as well - very clean, very aromatic, very light on the palate. My preference is for Saaz and Hallertauer Mittelfrueh, but many like Spalt and Tettnanger as well. Actually, I love Tett as well!
Hope this is helpful. Your best bet is to do what you can to not degrade and/or evanesce the volatile oils, the fragrance and flavor oils. To do that, you need a short boil, or as I've described it, an intense slurry. Good luck, cool idea!