This procedure is pretty straight forward:

Use a nail or the back side of a pin to push the black holding part out of the remote.

Do this over a box or an area where the pin can easily be found again.

Remove the old cut key and place the new uncut one into the remote.

The hard part: getting the black pin to go back inside. I used my drill press to push it back. worked fine.

Go to the dealer or locksmith and have the new blank cut for your car's key.

Total cost:
25$ For the used remote with the key cut off.
20$ For the blank.