If you download the Hardware Maintenance Manual (HMM) PDF for that model, IIRC, it'll tell you step-by-step how to replace the fan&heatsink assembly. Follow those instructions, but after you remove the assembly, just remove the thermal compound, pull the fan off, tape the new fan onto the old heatsink assembly, apply thermal compound, and resume following the HMM instructions for putting the 'new' assembly into the laptop.
Edit: The latest version of the HMM I could find: https://web.archive.org/web/20210429114642/https://download....