The above questions and advice are excellent. The issue I see is what was mentioned about the wrap laying flat since it looks as though it is rather wavy. If it were me, I would seriously consider purchasing new wrap to ensure a better job.
When I rewrapped my drums with pearl wrap from Precision Drum Co (they are about 15 minutes from my home) they provided me with 3M Fastbond Contact Adhesive 30-NF.
It worked great. Just take your time and go slowly.
This was the method I used.....I did not glue the entire length to the shell just the starting end, which could be debated with pros & cons, but I wanted to ensure if I ever wanted a color change it would be easier without the entire length of wrap glued to the shell. Even gluing the starting end to the shell could be eliminated if clamped properly. Also ensure that the wrap is placed on the shell so that it will remain aligned with the shell at both ends.
I placed the starting end of the wrap under a row of lugs which is common - also place the seam on the side of the drum that will face the drummer to further hide the seam from sight as viewed from in front of the kit. I glued the one end of the wrap to the shell with about an inch length of adhesive and clamped it tight to the shell for a couple days to ensure a solid bond. I then slowly pulled the wrap tight along the shell, securing the wrap tight against the shell with clamps just beyond the next row of lugs. Then bore the screw holes for the lugs through the wrap and then attach the lugs to secure the wrap in place and finally remove the clamps (the lugs will hold the wrap so you can move on to the next row of lugs).
Then continue and repeat at each consecutive row of lugs. In this fashion, the wrap can be pulled tight against the shell between each row of lugs. At the last row of lugs, I applied another inch long stripe of adhesive between the layers of wrap and clamped it tight. The end of the wrap should lay under the lugs to help hide it - AND I'll repeat : plan ahead so that the overlap end is facing the drummer so that it is also hidden from viewing the drum from in front of the kit. Once the glue is set and fully cured, then bore out the last holes for the last row of lugs.
Also be careful when using glass glitter as the material can be more fragile and crack under pressure especially at the overlapped end of the wrap.