CPU cooler fan for old pc

Hello everyone!
So, I have a HP Pavilion M7680n set up as an htpc (mainly for light tasks, movies and office work) https://support.hp.com/lv-en/document/c00739902 -even after 11 years it still gets this job done (with a few upgrades down the road) and I will like to keep it going.
The problem I have is that recently the CPU cooler fan is starting to fail (It makes loud noises like the bearing is worn out and sometimes the fan takes a while to spin at startup). The Issue is that the Cooler Master fan is 92mm and mounts with 4 long (30mm) slim screws in the CPU heatsink(stock) which in turn is held in the socket by 4 screws in a plastic bracket (so fans with clips wouldn't work naturally). Could you recommend me a decent quality fan that could fit? (Sorry for not being able to post an image at the moment)

Thank you for your answers!
 
Solution
Update: I have installed two new 92mm Arctic F9 PWM PST fans in the pc (one for the cpu cooler and I also replaced the exhaust one as it was worn out as well). Unfortunately I was only able to use one screw for the cpu cooler fan and a bit of double sided tape-it helds just fine.
However, since this is prebuilt with a custom mobo I had to go into the BIOS to uncheck "Check system fan" message (since I plugged both 4-pin PWM fans in the CPU fan header as the fans came with a splitter and I wanted to use the PWM function on both fans).
Update: I have installed two new 92mm Arctic F9 PWM PST fans in the pc (one for the cpu cooler and I also replaced the exhaust one as it was worn out as well). Unfortunately I was only able to use one screw for the cpu cooler fan and a bit of double sided tape-it helds just fine.
However, since this is prebuilt with a custom mobo I had to go into the BIOS to uncheck "Check system fan" message (since I plugged both 4-pin PWM fans in the CPU fan header as the fans came with a splitter and I wanted to use the PWM function on both fans).
 
Solution