Hi @laurat1989
like the others & yourself, I am concerned about getting away from those exhaust gases.
I would definitely go through the timber wall, with a hole as small as you can get away with to prevent exhaust coming back in, but also large enough to allow heat to be kept away from the timber. I'd suggest fitting a metal flange that will allow the pipe to go through and wrap it in tape (as already suggestioned).
To get the exhaust away from people, I suggest mounting a length of metal downpipe on the other side of the wall such that the muffler outlet can rest in or near its opening. You'll need to mount the pipe so that it's clear of the wall though, as it needs to get warm to work as an exhaust remover. (Explained below.)
I suggest some metal hooks such as Everhang 50mm Zinc Plated Square Hooks, staggered a little so the pipe won't swing sideways.
https://bunnings.com.au/applinks_p0046411
Buy longer if you can find them.
Tie downpipe to hooks with stainless steel cable ties.
The idea is that the hot exhaust gas will heat the body of the pipe, which will cause an updraft in it to draw the exhaust away. Don't seal the muffler to the downpipe (or whatever pipe you choose) as this could cause the device to malfunction (it's not an exhaust pump) and it needs a little fresh air coming into the pipe to help create a good updraft.
This is the same principle that the old Metters wood stoves used, to get hot air from a fire sitting above the oven to flow down and around the oven, then up the hot flue.
