Most chips that have a hold-down of some kind heatsink, I just use a paste/compound. The Noctua paste is "cheap" and effective. I use it on pretty much everything. VRM and memory still get pads, though. Usually because something NEEDS to fill the space.
I'm noticing now, that heatsink looks like it was soldiered on, but does have an "easy target", mounting it flat with paste should be do-able.
If you're paddin', pretty much ANYTHING is better than the stock one. I would indeed go with the thinnest one.
Main Loadout (daily drivers):
Intel TE430VX, Pentium Sy022 (133), Cirrus Logic 5440, SB16 CT1740
ECS K7S5A, A-XP1600+, MSI R9550
ASUS M2N-E, A64X2-4600+, PNY GTX670, SB X-Fi Elite Pro
MSI Z690, Intel 12900K, MSI RTX3090, SB AE-7