I've done two windshields jobs in the past two years- one for a friend that had a lot of rust. For his, I used the rivets, with a piece of cardboard against the windshield for protection. Being an amateur riveter, it was a PITA, but I got it done.
Last week, for my rig I did something a little different. Backstory, I acquired my 99 back in 2004. It had a replacement windshield that for all intents was a good install. This 20 year old windshield finally cracked, and when I removed all trim pieces I was surprised to see they used plastic body fasteners (ribbed version) to secure the side trim. The trim was very secure and the windshield frame had no rust.
So, I set off on finding a close replacement for the fasteners (ordered some from Toyota that weren't a match). ACE hardware was the source of what finally worked. I trimmed the edges of the circular top on the fasteners so they would fit flush in the channel. I'm happy with the result and trim is tight.
Also, order your trim pieces from Partsouq if you want to save a bit. $77 versus $189 for a single side piece. Order some more stuff from Partsouq to further defray the $60 shipping. Five day delivery. I ordered the two pricey outer channels, two inner trim strips that cover the fasteners and the top trim rubber strip, so 5 pieces total for the job. Cheers.