I don't mind at all. You would embed it in the under structure (the foam or plastic whatever you built the body of your puppet out of), I'd suggest either just above the paws or just under the knee.
However, on further reflection I think the fishing line would be a better solution. Not only...
While I was patterning the skin for my first puppet my wife leaned really hard on my shoulder and asked, " When do I get one?"
Same rules apply as with Brewster it's gonna be a while before we complete her.
The winter Holidays are killer at work, plus I got married and moved into a new house so Brewster had to be put on hold. January is kind of a dead month so I was able to break him back out and built his hands!
You could give him a vampire collar perhaps to cover the back. I'd suggest including the hand/arm sleeve in future designs. Maybe a "Groucho" nose? I'm still digging the idea of an incognito alien visitor.
I like his concept, and the Easter eggs for eyes work well (I found some that split longitudinally that I plan to use similarly). His jaw may be hinged a little too far for my personal taste. I'd probably recommend a complimentary color, or even the same color as the mustache, for his eyelids...