Emmett,
Those amazon items look OK. You need 3 1/2 minutes according to information I've read. Then another 2 minutes cool down time. If I use more than a 1/4 teaspoon or 1 gram for non US folks, I will leave it run for 5 min then unhook from one post on the battery (I use a small lawn mower style) to get a full burn. Be aware you will likely scorch your solid bottom board, not so much on screened bottom board. My 10 frame boxes are screened but my 5 frame nuc size are not. What I do for the nucs is I use a shim with a hole drilled at the bottom 1/2" seems OK. I put a 6" x 8" piece of aluminum flashing on the top of the frames, set the loaded wand on the flashing, set the shim over the rod of the vaporizer turn the solid top upside down on top of the shim then turn the unit on. Place a towel over the front entrance.
I don't use gloves but I do use a respirator.
With no capped cells 1 time should kill any and all varroa. I'm getting ready to do my OAV on my colonies today or soon. With capped cells I will do every 4 days x 5. This goes through the whole brood cycle or 21 days. I'll do an alcohol wash to see how I'm doing after the second time. Last year I did monthly OAV and had good luck with my big colonies, not so much with the nuc sized one.
Later in the year, August and September is a good time to do OAV again so you have healthy bees going into the winter. That will help them make it through the winter successfully. Consider the 4 x 5 schedule at that time.
Glad to hear that the queen was successfully got your queen released.