Like most things, I think it'll mostly come down to your personal tolerance (in this case, for wobbliness). For me, I think that - with good quality keycaps and switches - the biggest problem will be the keycap 'swivelling' (like a propellor) rather than 'see-sawing', even though stabilisers are probably most often associated with preventing the latter. I tried a 2u key in a switch tester just now, and it pressed firmly and felt very adequate even when I pressed on the very edge - I was actually surprised by just how well it did. Though when I nudged the keycap around with my finger, the 'propeller swivel' was very noticeable. This would personally bother me more, as switches moving around while my fingers are resting on them makes a keyboard feel cheap and rickety to me.
But in my experience, by far the most rock-solid stable 2u keys are the ones mounted on 2 separate switches, rather than 1 switch and a stabiliser; I have quite a number of these between my main keyboard and macropads. You can't use a regular keycap with 3 stem sockets, but need a so-called 'POS (Point of Sale) style' keycap that has 2 sockets. Some keycap kits (eg. Ortholinear kits from pimpmykeyboard) come with both, so I had the chance to try both and realised the POS mounted ones feel more solid. Just the other day I was finding one of my stabilised 2u keys annoyingly rattly, and specially replaced it with a POS keycap, and it made a big difference.
The main challenge with doing this, however, is finding sufficiently light switches/springs for it, since you'll be doubling up the spring weight. You can remove the spring from one of them and it'll work ok, but the asymmety will be noticeable. So far, gateron silent clear switches are the lightest switches I've found, and I've put the lightest springs I own into them (45g), but it's still a little heavy, and I have some 35g springs in the mail.
You'll also want to disable one of the switches, of course. You can do this in QMK or whatever remapping software the keyboard uses, but I find that it's easiest to just bend one of the pins to render one of the switches dead. This is the most fool-proof and reliable method, as even when you disable the key with KC_NO in QMK, certain features (eg. tap/hold combos) still don't seem to work properly when there's a switch physically there.