Walt:
I believe I'd be using 3M General Trim Adhesive, Part Number 08088. It's a clear, high strength adhesive. It's heat and moisture resistant. Comes in an aerosol can. Best part is it's available at your local Walmart for $9.88 a can. Walmart stock number 10-2008.
I use the stuff all the time. I use 3M black weatherstrip adhesive as well, but I believe for your application, the general trim adhesive will work better and you can mask off where you don't want it and spray it on.