My son is selling me his computer with has XP installed but I particularly want to retain my 98SE with existing programmes and settings. My idea is to get him to switch the hard drives from the old machine to the newer.

Would this work? What are any potential snags?

   I thought I already answered this.  I will try again.
   Windows XP is on the harddrive on the new computer.  If you take that drive out and put the old drives in, it will no longer have Windows XP.
   If you install the old drives in the new computer exactly as they were in the old computer, when you start the new computer, it will run Windows 98.  It will run just like it did on the old computer.
   If the monitor is different or other hardware is different, there may be some problems.  Some of that may just be Windows asking for the driver.

There are other possibilities.
1. If you have the installation disks, there is a good chance the programs may install on WinXP. If not, there are 'DOS Box' programs and Virtual Machines that may allow you to run them in a Win 98 environment.
2. A migration program such as PC Mover allows you to move programs with their registry values to a new system. The site claims to move files for systems all the way back to Win 95.