Just use consistent pressure and take your time. The only thing that can happen is either the pad comes off the plate or the sticker pulls off the drive.
My issue with the adhesive is placing the drive and mating the pad to it while aligning the screw hole.
Mine's a bit more modular and the top one is a PITA w/ the CPU cooler overhang. There's the bottom and middle sockets though that are easier access but, they're still a pain to get access to if it's inside the case. Having used N VME drives w/o these plates I don't really see the difference they make in temps IRL. They're mostly for looks IMO. With proper airflow they might actually hinder cooling of the drives.
If there wasn't 5 different sizes of M2 devices it would be a better idea if designers just went with a quick release like RAM. My laptop doesn't need a heat sink on the drives nor did older systems. It's a bunch of hype unless you're really pushing the drives constantly with data. Mot of the time though these just sit idle and temps are ~40C. If I have to dig into my setup in the future I would just remove them and only put the screw back to hold the drive in place.