I'm not sure of the exact layout of a 1650 but I would definitely order a replacement screw(s), in general, anything cooling wise needs even pressure to get good thermal contact, depending on where the screw is it could mess it up and run hotter than it should. also always a good idea to buy a magnetic tray when working with small parts
Get on HP's support forums and ask what the size of the screw is before anything (99.99% chance it's a metric screw). HP's support forums are full of knoweldageble people including paid HP tech support people. I've used them for years when asking for help rebuilding laptops and missing screws and have never been let down. And no, don't run that GPU without full screw lockdown as another said here. GPU chips like CPUs have irregular hot spots and if your missing screw for the heat sink clamps down to said hot spot, you are risking burning up the card under load.