trying to match a small engine muffler- Kolher Xt775 muffler 14-068-08-S

While that looks rather universal sized, one cannot say for certain based on a picture. So I'd say you need to pull the muffler and risk breaking the bolts so you can see if indeed there is a pipe thread there in the exhaust port. You could also also measure the bolt spacing and see if it matches up to the similar type mufflers sold for Briggs and such at Home Depot and hardware stores.

As for finding an actually quiet muffler, that invariably seems harder. No experience with this particular group, but they are billed as being quiet. http://www.jackssmallengines.com/Products/Quiet-Mufflers

Used to be small engine mufflers were fairly universal so it was easy to find something. Not so much nowadays. My dad works on small engines and most do not have the pipe thread anymore, so that may not work for you.

Maybe pick up some noise cancelling headphones, if you can't get work to fix the problem.

This one is $6 if you can wait for it to ship from Pluto:

http://www.amazon.com/Bolt--Muffler-Kohler-Replaces-41-068-08S/dp/B005HAA7ME/ref=sr_1_fkmr0_1?ie=UTF8&qid=1454692012&sr=8-1-fkmr0&keywords=14+068+08-S+muffler

If you could get the bolts free...

You could try fill it with steel wool as a packing material to quiet it down.

Cheapest solution would be to leave the stock unit alone and weld a universal 3/4" NPT muffler to the outlet. Add a bracing strap from the new tip to the old muffler body to keep it from breaking off.

Check to see if the block is threaded. Years ago when I was teaching shop I used one like this to be able to run a small gas engine in the shop. It was threaded on both ends so I just ran the outer end out thru a window.