Get another external hard drive and format it suitably.
Problem is its a new hard drive. only a few months old
Still. I suppose you could format it as two partitions.
What kind of system drive? How big?
You may not need an external scratch disk at all, if the system drive has enough capacity - and you keep your working archive elsewhere. With spinning drives the general advice was to have a separate scratch disk, but SSDs changed the rules and there's no particular reason to do that now.
In any case, an external 250GB SSD isn't all that expensive nowadays. Of course, there's a limit to how many external drives you want to keep track of...