This harder to explain than to do.  Use thumb and forefinger of one hand to squeeze the stylus on the two stylus guard hinges, use thumb and forefinger of other hand to hold the cartridge body.  Now pull them apart, no need to be gentle.  The stylus comes straight out of the front of the cartridge body.

Here ya go! Easy peasy!

Thanks, I think I have been overly intimidated by the word "gently".

Worst case is I might damage the old stylus - the cartridge body looks robust enough ...