Holy moly! I wouldn’t do that to myself and I’m an experienced knitter. You’re working on some heirloom-quality complexity here. I’d find a scarf or wrap or something else with a much larger yarn for my first beading project (I used light weight the only time I did beading–it was a small pouch to hold a handmade string of prayer beads). Or do a bookmark or something simple so you can get used to working with the yarn, needles, and beads–all three of these are going to prove a challenge on this project. You’ve probably also got some complex finishing and attaching a clasp at the end, too. I don’t want to be a Debbie Downer, but I’d hate to see you quit knitting because one of your first projects was a discouraging experience.
How tiny is tiny? You can get wooden needles as small as size 0 (I feel like I had a pair of wooden 00s a while back before they snapped) but you’ll probably have to order them online and I bet you’re using something like a 0000. Wood is grippier but you’re probably stuck with metal in the really tiny gauges.