Here are my suggestions:
Families and Friends
You trace and mail your hugs to various Special Loved Ones. Yes, one of the kids will have to trace you. Giggle fest!
When those SLOs get their hugs in the mail, they – the SLOs – have to rather immediately flop on their backs and do the whole tracing and mailing thing, mailing their hugs to a new set of SLOs. That third group sends off its hugs to more People In Need Of A Hug.
It’s a chain mail hug!
Instead of mailing these hugs, line up the hugs from fingertip to fingertip around the room. That’s gotta be good for multiple awwwwwws from the parents, yes?