No. The back lash is internal between the ring and pinion gears. If you just swap the axles, you won't be messing with the gears in any way.
I would just remove the covers, clean the housings out with brake cleaner, do a good inspection of the gears (don't remove or loosen anything, just look), replace the covers, and refill with new fluid.
Once you have the 4.10 axles installed you will need to bleed the brakes.
Keep in mind that free advice can frequently be worth less than you pay for it.