You can't swap out anything without removing the back. It might be possible to refinish the frame but it would be a mess and could possibly damage something.
It's either go all in and take it apart or leave it alone.
A meeting in the middle might be photo documenting the entire process, creating a photo sheet, removing, cleaning, re-matting in a cleaned frame or replacement frame/shadowbox and attaching an envelope to the back of the frame and inserting the photo sheet with completion signature and date.
I say that because a museum wouldn't leave it as is in that frame.