Clark:
You will have no problems firing them in your full-nitro double, other than regulation of course!

The 'BP' designation simply means that they have a thinner jacket than the bullets designed for the full nitro load. They are designed to be easier on older soft barrel-steels, and to obturate better in early rifling patterns like Henry rifling. They also expand more reliably at the lower BP or 'nitro-for-black' velocities, so expect them to be absolute bombs on thin-skinned game if driven at full nitro velocities!

I shoot the 650gr Woodleigh 'BP' bullet in a vintage ULH .577 black powder express double with Henry rifling, and a modern Greener-conversion with brand new barrels. Works perfectly in both.

BTW, here's a picture of the difference between the 650gr Full Nitro Woodleigh and the softer 650gr 'BP' version, both driven at about 1665 fps into unsuspecting buffalo! I'm sure you can guess which is which!