flrflr wrote:
I have unfortunately used both hard drive as a TimeMachine backup so can’t use them. Is it a better option to replace the harddrive in the Mac by removing the old one, or is it better to use an external one (in which case I welcome brand recommendations)?
Many thanks
You can restore a Time Machine backup to an external drive, that would then be bootable. Whether or not you want to do that (i.e. sacrifice one of your drives by reformatting it to eventually turn it into a bootable external drive) is up to you. As was stated by Kappy there's a recovery volume on a Time Machine backup that will give you the full suite of utilities including Disk Utility, Restore from Time Machine, etc.
You could also access this suite of tools using Internet Recovery. Instructions are here:
About macOS Recovery - Apple Support
I would suggest getting a new drive and installing it yourself, but not everyone is comfortable doing it even though it's relatively straightforward. But if you just want to get started quickly using an external boot drive, you can reformat one of your Time Machine drives using Disk Utility (Erase function) and then restore your Time Machine backup into a bootable volume using the available utilities.