Back in the days of GP I oils, early wide spread multi viscosity oils, early viscosity index improvers, there was a problem. Things have changed.
Your little engine would be no more or less prone to mechanical shear than an auto engine. Its oil capacity, compared to an auto sump capacity, and compared to the extra mechanics of an auto engine, would be proportionally close.
Check out the oil temperature threads in this forum. The oil in your engine probably doesn't get as hot as you might think. However, your engine will have hot spots, where air doesn't flow and oil doesn't circulate that well(splash system) This is where the recommended full synthetic really shines.
We now have conventional oils that are GP II/II+ hydro-cracked base oils. They have a higher natural viscosity index than previous base oils. They need less VII to achieve the same spread. The viscosity index improvers are also much improved. They don't shear as badly. They still shear, just not as excessively/quickly.
Pennzoil 10W-40 is reported to be a GP II+ base oil. I don't remember what the high temperature high shear number is, but I think it is near 4.0, which is good. It is also probably higher than the straight 30, mono grade oils that are often used in small air cooled engines. Even an oil with no VII will shear on the molecular level. It has to do with the molecules and their bonding/elasticity. Nothing to try to remember or be concerned about but even an oil with no VII is not immune to shear.
I use 10W-40, full synthetic oils, in my air cooled turf tractor,(14 HP) air cooled lawn tractor,(20 HP) and air cooled trim mowers, (5HP and 3.5 HP). The oldest is 19 years old and still used every week.
Someone said the Pennzoil YB 10W-40 would not be the best choice. I fully agree, not the BEST choice. It is, however, a fully workable, fully usable choice.
I would NEVER take even a full synthetic, GP IV motorcycle oil to 40 hours, but that is just me.