That should work fine. I often use a a sheet of paper I've fully exposed and developed so that no extra light is transmited though the burning mask. These are generated from accidents like forgetting to stop the lens down, or exposing with the head in white mode...Does plan old grey card board suffice? OK, thats what I use and there is enough for me to see the image
I've never noticed a problem with other reflections, though I've never tried to test for this rigorously, maybe ignorance is bliss.
If you're using a largish sheet for the mask, then it's shadow is protecting the paper from most stray light.