I’ve used the ultra fine scotch pads for years and they are fine for hitting finish between coats, but I wouldn’t use them to tame a gloss finish down. The 0000 steel wool is the way to go for giving you a hand rubbed satin finish. After you rub it down use a cotton rag to polish it. You won’t damage your finish rubbing it down by hand. Been doing it for many years….
I use a high gloss auto clear coat to spray all my bows, but I spray a fine Matt finish which gives it the satin look. Occasionally it’s a bit too shinny and can be easily rubbed out. The last thing I’d do is spray a satin poly over an existing finish…. You are just looking for problems there….
Kirk