Anything that you can stick in there that reduces the outlet size will reduce the sound.
Usually baffles are a smaller diameter perforated tube with end caps that fit inside the exhaust and mount with a set screw from the outside.
Here's one as an example without the perforated core
This is likely something like what you saw.
The set screw is there so it can be removable. If you don't mind it being permanently installed, a couple spot welds could be placed inside the exhaust to hold it in place.
You could always grind out the spot welds if you needed to remove it.
I would get a very accurate measurement of the ID of the muffler, give the dimensions to someone that could weld up an insert like that. test fit it to see if you like the sound and spot weld it.
Usually baffles are a smaller diameter perforated tube with end caps that fit inside the exhaust and mount with a set screw from the outside.
Here's one as an example without the perforated core

This is likely something like what you saw.
The set screw is there so it can be removable. If you don't mind it being permanently installed, a couple spot welds could be placed inside the exhaust to hold it in place.
You could always grind out the spot welds if you needed to remove it.
I would get a very accurate measurement of the ID of the muffler, give the dimensions to someone that could weld up an insert like that. test fit it to see if you like the sound and spot weld it.