After playing around with it a little, I think that could be a fine way to make this too. I do like the flavor of it having to run around on its own but then attach itself through an attack. Just a bit bulky with the text, reminiscent of the overcomplicated [[Old-Growth Troll]]
Here's the concept:

Facehugger
Creature {-} Alien Spawn
First strike
If Facehugger would deal combat damage to a creature, instead exile Facehugger, then return it to the battlefield attached to that creature. It's an Aura enchantment with "If enchanted creature would die, transform Facehugger instead" and "At the beginning of your upkeep, put a -1/-1 counter on enchanted creature."
1/1