I hope someone else has a better solution but the only thing i can think of would be to check the size of the p6ws.war file and then download the patches from oracle again and compare them to see which one matches up.
Check BREBootstrap.xml in the P6 Web service folder. If the database was reconfigured after installation of each service pack or fix pack then that might give you the idea.
Timestamp of p6ws.ear could be another way of identifying by comparing it with the patch release date.
However I guess when in doubt it is always better to reapply the Web Service patch matching the application version.
I thought of the timestamp as well but given most P6WS patches require running the updatews batch file I wasn't sure if this would be reliable.
Similarly with the bootstrap version i've seen a few KB articles recently around this not always updating properly with patches so this also might not be the most reliable method.
Agreed that re-applying the known correct version for the database is possibly the best approach.