You’d get away without the latest trials tyre which would wear too much at full retail price. A TS 125 is not going to overpower one of the older fashioned trials tyres on the road (still produced in tubed form for the older bikes but not by Michelin). Do a bit of Googling and go for one of those berated by us trials guys as not providing enough grip for competition use – it’ll be comparatively cheap.
A trials tread (made of ebony in comparison with the stuff now available) worked perfectly well in decades of the ISDT until they allowed knobblies so will provide all the grip you need for sensible trail riding.
The alternative is to use modern stuff discarded by trials riders when the blocks get a bit rounded – you can have four from me at a tenner each!
Ah yes towzer, I remember the good old Barum “pineapple” – but it was cheap from Bill Brown.