stumble
walk with difficulty

e.g.


"walk on shaky legs" seems to be reserved for young animals.

Hm, Mr. Google spuckte im Zusammenhang mit "shaky legs" gerade auch reichlich menschliche Probleme aus. Klingt auch irgendwie passend. Kann ein native speaker was dazu sagen?

walk unsteadily
or hobble, limp, stumble
shaky legs I'd see as tremor, involuntary spasms rather than weak, unsteady
but I'm willing to be convinced otherwise

Ginge "She walked on unsteady legs to the bathroom"?

Yes, that would work, if the context is right. I think it sounds slightly more literary than "walked unsteadily".

Alternatively: she tottered [unsteadily] to the bathroom.

Thanks a lot.