Shot peening aluminium alloys is used in the aero industry. The "shot" I saw being used at Metal Improvement Derby factory for peen forming wing panels was about 6mm diameter and projected with very little force, almost just dropping, to produce the curvature required.
I think shot peening in the home workshop would require a lot of effort to achieve good results, not impossible, just time consuming.
I think that you will find designs for peening guns and flap wheel shot projectors on the internet which could be made at home. The biggest problem as I see it is controlling the intensity of the the shot impact consistently.
MIL-S-13165C gives quite a bit of information on the process and measuring the intensity, but is more commercially based. The Metal Improvements website has some down loads which may help you.
The shot used in the peening process is not just steel, but can be glass or ceramic beads. I'm not sure were you would source the media, but you will need quite a lot of it. After the shot has been used it goes through a system that removes any broken or deformed shot, which would damage the work if used again, as well as sorting by shot size.
Shot peening is a messy process, years ago I attended the opening of Metal Improvements new factory at Newbury, I was told that this would be the only time that the floor would be free from shot! Do consider that the shot will go everywhere.
I hope this helps a little.
Neil