In this case it does matter. See SAE J300. HTHS of 2.9 vs 3.7 matters a lot in high temperature / high load applications. Just ask CUJET about all the rod failures on generators running 5w-30 after hurricanes in Florida. 5w-40 is just a 5w-30 on mild steroids; it's not anything close to a straight SAE30.
I like 15w40 but I don't think any of these engines are picky, contrary to what anyone else has to say.
usually have 15w40 laying around extra, but I wouldn't go out and buy something special for any of my small equipment.
Then again, I hardly ever change the oil in my generators or pressure washer as they only run a couple hours a year.
Lawntractor gets it once a year.