Can I just add something to what BM has said (he starts work earlier than I do ) :o)
That set up should be fine. Although the unit wouldn't have a balancing valve as such ............the very fact that it's thermostatic, and you can adjust to either the hot or the cold side, that will give you the "balance" you need. Don't be tempted (price) to go for a non thermostatic. They are not much more than a crude "diverter" from hot to cold................... getting a good balanced temp with them becomes a case of micro-fiddling to keep a steady temp.