Almost certainly yes to using different size collets if such can be got. But identifying the collet size and type will probably be challenging.
I believe Procunier and (some?) Ettco metal collets can still be bought new but there are a number of variants which rapidly get confusing. Fortunately most are obviously different when you look at the picture or drawing.
Tapmatic use a cone device that looks very similar to Jacobs Rubberflex, but much smaller. The inserts can be got for approaching £50 via MSC, example here **LINK** . Suitable holder looks like something that could be made at home, basically a conical receiving hole with a suitable screw on cap. Well into "how badly do you want this" territory.
All but the very smallest Pollard (licence built Ettco) heads have a simple chuck to hold the tap aligned. Looks just like the old style cheap hand drill ones. Three triangular jaws spring loaded apart in a screw-down cone. Does the deed just fine as the actual driving is done by the square.
Retro-fit may be possible if the existing drive end can be removed.
Simplest way is to make some tap carriers to fit the existing collet. If yours has a square driver that closes right up, like my Pollards, a simple split sleeve around the tap shank might suffice. Probably need to be afairly long tap tho'. Dunno that I'd care to go below 3/16 " or 5 mm with ahead that size tho'.
Clive