What motherboard?
What gpu?
What psu?
If you are reading the speed with nothing running, the cpu is just idling. Run memtest or Intel Burn In and monitor speeds through cpuid and/or hardware monitor.
You really don't want to remove the cpu when you switch over to the noctua. Leave the cpu clamped and GENTLY twist the stock cooler side to side to break it loose from the TIM. DO NOT use force - you don't want to bend the pins/socket. If you cannot get the cooler loose, run Intel burn in to heat the cpu and TIM and gently try again. Worst case if the cooler won't separate, then remove the clamp and CAREFULLY lift the cpu/cooler out. Cover the cpu socket with the plate that came with the motherboard. Then gripping the edges only of the cpu, twist the cpu off of the cooler. Do NOT touch the base of the cpu.
Once you have the cpu free, gently clean the top of the cpu (holding the edges) to remove old TIM - I use 91% isopropyl alcohol and a lint free rag. When the cpu is clean, carefully reinstall into m/b. It should drop in - no force whatsoever. Make sure you get the triangle on the cpu lined up with the corresponding mark on the cpu socket. Once the cpu is correctly inserted, lock it down with the clamp and then install the noctua. Be sure to snug up the mounting screws of the noctua - that sucker is heavy and will tend to move around in a typical horizontal mounting.
Mark