I'm not sure if I've understood this correctly.
If you replace a part like a caliper. Bleed as you normally would, either 2 person manual job or a 1 person pressure bleed. Once you are happy the air has gone. Make sure your brake fluid level is on max and pump the pedal to force the pads out to the discs. Re-check level and you're done.
I somehow suspect I'm missing something here?
I feel that I'm missing something as I agree entirely with the above and can't see what the issue is.
As said above, if you've replaced a Caliper or piston, bleed the system as normal (2 man or 1 man Eezibleed Kit) and when you have done that you are in exactly the same position as if you had retracted the pistons to change the disc pads, ie. the Pistons are out, as in not touching the brake pad against the disc, You then check the fluid, press the brake pedal, check the fluid again, and press the brake pedal until normal service is resumed.
Certainly no special tools needed.
So, new Caliper on with disc pads fitted (with the pistons retracted as they would be if you'd fitted new pads), bleed brakes to fill Caliper with fluid (using Eezibleed if working solo), check fluid, pump pedal to push the piston out until solid, check fluid again.
Apologies if I'm missing something.