I think regulations specify a quarter inch (~6mm) thickness limit for letter rate. With minimal padding, it'll be close. May depend on which clerk is at the counter that day.
FWIW if you leave off the spring you could post it in a photo mailer for $1.15 worldwide. Cut a hole in foam sheet and tape either side. Max thickness 1/4” and be sure the foam is at least as thick as the board( might need two layers). Great giveaway WH. I’d have entered but I’m already way behind on projects and hate acquiring bits and not using them.