Hi Liz Don,
I had my left hip replaced in 2014 and recovered superbly with certainly no limp. I am due for the right this coming Tuesday.
After the left was done, I used two crutches regularly for 4 weeks, for gait training. Perfect steps, perfect posture, practice practice practice. Abs in, shoulders back. I did this well beyond the point that I needed the crutches for support -- it was all about posture and gait training. Lots of walking with the crutches.
After I was done with the crutches I switched to two hiking poles -- there are videos of this if you search for Nordic Walking. This is awesome, helpful for more effective cardio training, and once you are able to do so they are excellent for hiking in steep terrain, should you desire to do so.
For me personally, one single support like a cane was not helpful in reminding my body to be even, but everyone is different and you should use whatever helps you. They're just tools.
Kind wishes for continued healing