No, you want to air dry the skins. No tanning needed.
I got my skins from Mike Yancey, Pine Hollow Longbows. I was in the process of refinishing the bow already, so I knew the limbs were clean and free from grease, oil or foreign matter. I roughed up the glass with 100 grit, wiped clean with Acetone. I then applied a thin coat of Titebond III. Place your skin in a pan of clean water, put another thin coating of TB III on the limbs, pat dry the skin and place it on the limb. You have some time to get the skin exactly where you want it, press out all the air bubbles with your fingers. I go back over it about every 15 minutes or so just to make sure some spots don't lift off.
After the limbs are completely dry, (I waited a couple days) I take a firm sanding block with 100 grit and carefully trim the edges. Once you get the edges trimmed, take duct tape and press it on the skins to remove all the scales. Make sure the scales all come off or you'll get a crappy looking finish.
Apply your favorite clear finish to the level of coverage you want and Voila!