In order to save Replays in TF2, one needs Quicktime. I have several other codecs installed on my system, is there any way to make TF2 use them?
It is not possible to force TF2 onto a completely different codec. Valve have said in a forum post a while back that they will look into whether they can come up with a different solution for Windows users, but for now we are stuck with it.
However, according to this Steam Community Guide, you can use Quicktime Alternative instead of installing Quicktime. It's a set of free codecs for playing/watching Quicktime video without Quicktime, and apparently works with TF2. (Use at your own risk):