RE: Silencing a speed bow.
If it was me I'd get a schematic of how it's supposed to be before going any farther. Then I'd get the parts and a (the right) press and new strings and do it myself. Before you take it apart take pictures and video the disassembly, possibly doing only one end at a time.
If you have to pay someone who has a working one to take pictures of there's. Be best if you can find someone who works on there's.
I have never been in a shop that knew what they should know. Most just sell them and can screw something onto one, some can even put new strings on, sort of.
At the very least find out what is wrong before taking it in. I don't nor have I ever own a BT so I'm no help.