I theory I think the minimum needed would be a new casette and 10sp shifter though I think its more complex than that but I could be wrong!

the more I think about it, the more it makes sense as to those being the only things. The 10sp cassette occupies the same space as a 9sp so the only problem would be getting the indexing right as its fiddly even with 9sp sometimes

would there be a need for a new chain??

This is where it falls down.

If you need a new thinner 10 spd chain then surely you might have you have a new ring up front too. How would the new chain cope with the jockey wheels on your 9 speed mech?

I agree with highclimber re: the cassette occupying the same space so it's all about indexing with the shifter assuming no chain issue.

So with actuation ratio the 10 speed specific shifter is pulling more or less cable for a certain distance of movement in the derallieur than the current 9 speed shifter, so you'd never be able to index it correctly with a 9 speed derallieur and 10 speed cassette?

from my own experimening on my 1×10, your 'regular' 9 speed, or road rear mech would work but only with the 10-speed flatbar shifters.

Once you have (dyna-sys) XT 10 speed shifters then you do need a new 10spd rear mech too, not even a 10 spd road mech will work.
Am still experimening though as one of plus points to me of 1x is to have a nice short cage rear mech. The new DynaSys XT rear mech has a seemingly very long cage….
For info, I am using a Sram 10spd road chain and an E13 Guide Ring