Regarding perspiration and the removal of perspiration stains and related odor from wool suits, it's important to recognize that dry cleaning solvents and fluids are primarily used to emulsify oil-based stains such as body oils, lotions, creams, cooking oils, etc.
Perspiration (and related salts and acids), on the other hand, is a water-based stain and no amount of dry cleaning can remove water-based stains. (Other examples of water-based stains include, soda, coffee, beer, wine, juice, etc.). Given that water-based stains don't "dissolve" in dry cleaning, a skilled stain technician must remove ALL water-based stains by "flushing out" the water-based stains BEFORE the garment ever enters the inside of a dry cleaning machine. If not, the acids and salts from perspiration remain in the fabric causing the fabric to smell when the underarm areas "warm up" during wearing. Furthermore, perspiration coupled with certain antiperspirants causes the fabric to "rot out" over time.
One way to tell whether your dry cleaner has removed the perspiration from a dry clean only garment is to hit the underarms with a source of steam (say from a hand iron). If there is perspiration in the underarms, you'll definitely smell it.
Suggestion: take your suit to a cleaner that employs skilled stain removal technicians (caution: most cleaners don't). Make sure that they thoroughly flush out the underarms prior to dry cleaning. Flushing is equivalent to washing the underarms multiple times on a spotting board using a strong jet of steam from a spotting gun.
The longer the perspiration remains, the more difficult it will be to remove all the perspiration from the suit coat. Just one more reason that caution should be exercised when buying "gently used" suits online. The suit may look great on the surface -- no stains, no moth damage -- but the odor can sometimes be overpowering and extremely difficult to remove despite multiple attempts at flushing and cleaning.
Hope this helps sift through the option that have been suggested.