I haven't done any SAK mods for a while, but 10 years ago getting hold of 2.2 mm brass rod was always a bit like sourcing rocking horse pooh. Don't know if there is a widely known supplier these days but here is a link to some I found recently.
https://www.aliexpress.com/item/1005008591776795.html? MAKE SURE YOU SELECT THE SIZE YOU WANT AS IT DEFAULTS TO THE 0.8 MM DIAMETERI bought five sticks that are 500 mm long (20 freedom inches) and now that they have arrived I've measured them up and they are bang on 2.2 mm diameter.
So I now have more than I'm likely to use in the rest of my life.

Also got five of 2.5 mm x 500 mm from this link, as it was about 30% cheaper (but they don't have 2.2 mm).
https://www.aliexpress.com/item/1005007324267596.html? with this listing you have to select both required length AND diameter before adding to cart.Actually there is tons of modding supplies on Aliexpress now, a lot of it is very expensive but some of the replacement wood or brass scales are worth a look.