In the past I have done some backyard offhand practice with a pellet gun with some added barrel weight.  I have also tried some Super Colbri .22 ammo in my Stevens 44.  Last week I picked up some CCI Quiet .22 ammo at Cabelas.  It is rated at 710 fps with a 40gr bullet vs 500 fps for the Super Colbri with a 20 gr bullet. 
The sound difference is negligible as far as I can tell.  The bullet impacting my bullet trap makes more sound than the report.  The CCI ammo lets me practice at longer range as well.  55 yds vs about 25 yrs.  I decided to see how it would shoot off a rest this morning and here is the result.  At $5.19 a box it affordable as well.

I have never had any problems moving from my silhouette rifles back to schuetzen or my flintlock set triggers.  My Ballard triggers were well worn when I got it and you literately could not touch the front of the trigger without it firing.  It was a side trigger rifle; just barely contact the side and fire at will.  Lots of guys that tried it could not do it.  I think it is an  individual thing; some have trouble with transitions and some don't.   

I am sure physical condition has more to do with offhand than practice.  I experienced this when I was having lots of hip trouble and only working partial days. Another shooter who asked me how to improve his offhand told me later the thing that improved his offhand the most was losing his job and going to work for himself as a general contractor.   Nothing like swinging a hammer all day to improve yoiur offhand   

I hate painting!  Especially 20 feet up a ladder painting under the eaves.  I knew I should have built a single story house.  I agree with Dave about shooting your schuetzen rifle.  The pellet gun just doesn't feel right.  That is why I was happy to find the CCI ammo.  It lets me use my Stevens in match configuration.

Jack

Trigger time is what works. Dry firing or putting a round downrange. Shoot enough so that you do not have to think about what you are doing.  The gun just goes off when the sights are right.  .22. air rifle, or centerfire.
That is why my shooting offhand sucks.  I am thinking about when to pull the trigger.  Not good.

Not sure if I posted previously or not(memory thing), but my Alaska hunt last fall came down to one shot that made 40 years of shooting and practice all worth it. The morning before flying out, I called a nice bull out to the edge of the river and across the river at 180 yards. I knew that to hold our timeline, I had to drop him in his tracks. Shooting off sticks in a gently rocking boat, I spined him behind the hump. He dropped with such force that his rack half buried in the hard mud and it wasn't until we had a full side quartered off that we could extract the rack to get my first good look at his 62.5" rack.