Safest way to attach seedlings to cork

[HarmoniaGardens]

I've got a set of Brassavola Nodosa seedlings that all fell out of their pots last night when I dropped their tray. Thankfully nothing is actually damaged. They've been growing in a seedling mix of orchiata bark and stuff (I can't recall), so I'm hoping it won't be much of a shock to the plants to mount them, bareroot to some corkbark.

I'm worried about attaching them with fishing line. I'd prefer to use a glue, but I don't want anything that may harm the plants. Any recommendations?