I don't think your wild ID will suffice. You better check with WDFW. I have an email from a state official stating what my trappers number is. 
Yes a wild ID# is OK. WSTA asked for this a couple years ago because WDFW was no longer issuing Trapper ID #s. It had become impossible for a new trapper to get a number.
A little history. Back in the 70s WDFW started issuing Trapper ID #s. Then at some point they discontinued issuing paper licenses at dealer and you had to get a license through Olympia. They issued plastic credit card sized licenses and each one had a permanent # on it for each trapper. The same number followed you each year and you were allowed to use that number as a trapper ID #
Then they decided to do away with the plastic license and go to issuing licenses through agents again. At this point it was not possible to get a trapper ID # so we asked to allow trappers to use their wild ID # as a trapper ID # and they agreed.
At this point you can use any of the three numbers. If you are old enough you have all three like me.