I recently had to obtain a V5C for a Honda CB400f that had been off the road since 1978. (when it was two years old)
I had the old style blue single sheet V5 which has not been a legal document for many years, however as that was my only proof of entitlement to the registration mark (which was no longer on the DVLA computer) I was more than a little reluctant to send it to them.
I made a good quality colour photocopy and sent that in with a covering letter, offering to send in the original if they insisted and explaining my reluctance to trust it to the post. (and the DVLA)
I got my new V5C no problem and never had to submit the original log book.
One question....does your bike show up on the DVLA vehicle search feature on it's current registration? If it does, getting a V5C should not be a problem, if not, try the photocopy route, it worked for me.
Mick.