The mint system will be cleaned so as to receive the contents of the W98/Peppermint system.
If I understand you right then you want to replace Mint on the existing HDD (keeping disk but changing contents)
with the dualboot W98/Peppermint system from the HDD in your 4th PC.
Your options would be:
Transfer partitions (disk to disk)
You would need to clone the W98/Peppermint disk onto the Mint HDD. Making sure the Mint disk is equal or bigger
than the W98/Peppermint disk.
Once cloned then run GParted on the (exMint) disk and expand partitions to fill the disk.
The win 98 install (as Mark pointed out) will complain like mad that the hardware changed and will most likely refuse to run.
Peppermint will most likely run OK but you might run into problems if your existing setup did use the UUID insted
of /dev/sda1 type.
If that is the case then (from a LiveCD) change the disk designations in fstab.
Swap Mint disk W98/Peppermint disk.
This would be the easiest option but you could loose out on (possible) benefit of transferring to newer/faster HDD.
The Win98 caveat still applies.