OB,
I used 1-1/4" screw nails. They are steel with some sort of silver finish. I've not had any issues with rust or corrosion due to dissimilar metals. Here's a link to what I used.
http://www.homedepot.com/p/MD-Building-Products-1-1-4-in-Silver-Carbon-Steel-Floor-Screw-Nails-1-lb-Pack-95638/100159731I first adhered the trim with sealant/adhesive. I used 3M 4200. The trim was temporarily held in place with shallow screws. After the adhesive set, I removed the screws, squirted some of the sealant in the screw holes, and hammered in the screw nails.
I don't have any real good pictures, but you can get any idea in these two. The first is along my door trim. You can see the screw nails above and below the latch. You can also see some of the sealant oozing out. I cleaned it later. In the second picture, you can see them on the wall cap trim installed on the galley sidewalls.


Take care,
Tom