Yes, this happened to me after a difficult 2nd hip replacement, and my difference is about 2cms.
I have dreadful co-ordination and balance anyway, and it took me almost a year to adjust. This is what I did: use or not as you think best, being aware that we all respond differently.
I use an orthotic raise (1 cm as 2 throws the foot out too much). In summer I use sandals with both an insole and an enclosed back (Waldlaufer or Padders). I also use these instead of slippers around the house.
I found a pool at a private gym where I could 'water walk'. I got water shoes, and put an orthotic raise in. I found this improved my muscle tone and stamina. I am also much better at doing exercises in the water than on land! This was just whilst building up, and I now just do some exercises at my local pool.
I used Norwegian poles for walking in the countryside, so that I was level and balanced, and I gradually built up distance. I'm afraid that 3 miles is the most I can do now, as any further does put too much strain on my foot - imagine that walking in a raise is like permanently walking in heels! But I am glad to be able to do some walking. I can't do uneven ground these days, and am grateful for country parks with their nice paths.
If walking more than about a mile, I still use the poles and wear walking boots for the ankle support. Otherwise, I don't have to use a stick any more, but I do have to wear firm supportive shoes.
Hope this helps.