Painting it would be the best way, but if you can't or the customer requires vinyl for some reason, I would take a good picture and print it out, next I would use a piece of transfer paper of the original print and use a fine felt tip sharpie to trace, then scan it into your software and use your tracing capabilies to turn it into vector. Works great for me!
You may have to do some clean up but 9 times out of 10 if you take your time on the tracing you won't have to at all.. just make sure your not using a marker that bleeds out on the paper..
For some reason it comes out ragged after clean up, i would go ahead and cut it on a scrap of black vinyl and use my xacto to hand trim and clean it up, then rescan and you should have a nice clean vector of the emblem.