As many of you know, I am not a fan of cleaning suppressors (I have altered my opinion with regard to .22LR). As a rule, you will cause more damage and shorten the life as compared to doing nothing other than cleaning mounting surfaces. Suppressors are not guns just as car mufflers are not engines.
Hydrocarbon based solvents do a good job on grease but do nothing for lead, carbon, or salts. They are best for gun cleaning.
Water-based cleaning agents should not be used on aluminum cans unless the suppressor can be disassembled. The reason is that most soaps will not rinse out of the recesses in the can and will end up causing corrosion (or galvanic corrosion if there are dissimilar metals). If you can disassemble the suppressor, ultrasonic cleaning in water is fine. Otherwise don't do it.
Simple Green, at least the version readily available, is an alkaline solution with a pH in the vicinity of 9. It will discolor, damage, or strip the anodize coating (not covered by warranty). Same goes for a number of similar agents. The soaps dissolve grease and salts left from the products of combustion. It generally will not loosen carbon or lead.
Lead can be removed with the vinegar-peroxide "dip," a dangerously toxic combination after use. It will damage aluminum. A far better and safer choice for lead removal is soda blasting or tumbling.
I cannot endorse the following for obvious safety reasons. On disassembled parts, I have been successful using 7% nitric acid heated to 120F in my ultrasound unit for 10-15 minutes. It both softens and dissolves carbon. Even with fairly long immersion, I have found no damage to 7075 or 6061 aluminum, 300 series stainless or grades 5 or 9 titanium. It will damage the anodize finish on aluminum. It will damage regular steel (as well as 400 series stainless) in that it removes the carbon. Coatings ("paint") almost always include carbon, and I would anticipate this mixture will strip coatings. Splashed, it makes nice holes in clothing, skin, eyes, etc. Again, don't use it on assembled suppressors -- only parts.
All this said, in my opinion, the only suppressors where one should consider internal cleaning are the notoriously filthy .22LR.