OK, yes, that was too much of a gloss. Effectively, you can make both dimensionless, by measuring position in units of √(ћ/(ωm)), and momentum in units of √(ћωm) (I’ve heard this called ‘natural oscillator units’). In terms of those, the uncertainty relation for a squeezed state should then be ∆x∆p = 1/2, of course.