I was being too hasty. The head does come apart.
What's even better is that I didn't need to buy anything. The head on my pump has a switch, so it can be used on presta or schraeder valves.
Interestingly, I discovered that the rubber seals (grommet?) for each aperture are identical, just inverted: the seal is narrow at one end for the presta valve, and wide at the other for the schraeder. All I had to do was swap them around!
The hastiness was me discovering this after buying a possible replacement seal at the lbs. It's the right diameter, but about 3mm too long. But it was only (only!) 70p, and I might be able to cut it to length when the time comes (another 10 years or so, based on the life span of the other one).