John, great Yes, plumber's putty! It's inert ["having or exhibiting little or no activity, esp. chemical activity"], and cheap -- but I wouldn't advise "filling it up." You don't want to press it in so deep that you displace the scion alignment, or fill in 'between' the scion and stock cambial union. Just get enough in there to keep the rain water out.

Then wrap the stock with something that either expands, like a large grafting band on a smaller stock, or 'cellophane-like' garden tying material. If nothing else, use 'good ol' electrician's tape - which is so stiff you'll need to run a knife blade down it (away from the scion base) to allow for expansion after the graft takes (a month or two after growth).

And remember to paint over that puttied top cut with a grafting seal, like the latex based, "Doc Farwell's Grafting Seal - elastic brush-on coating for grafting." You can find the plumbers putty at most hardware stores - cheap … but the grafting seal isn't. I'd call some good nurseries before you burn gas looking for the Doc.

Hope you make it to the Scion Exchange … being one who knows what a "Scion" is