You didn't mention the year, or if the bike was new or used when you picked it up.
The PW50 has always used an autolube pump to inject two stroke oil, not requiring any pre-mixing of oil & gas.
So, now the question is, did whoever told you to mix it @ 50:1; A. Knew that the oil pump has been removed. B. Was you typical arm chair wrench and just figured since the bike is a two stroke it had to be mixed.
IF the oil pump has been removed, do you KNOW that it was done properly? An unpluged oil line and a pump spinning with no oil in it will soon lead to a lean condition and eventual engine siezure.
IF the oil hasn't been removed and is operational, USE IT. We've all heard the know-it-all's running thier mouths about not trusting the pump, yada yada, but I've yet to actually see one just up and fail.
Have I seen someone put the wrong oil in the tank? Yep. Lottsa times.
Let dirt or some other contaminate get in with the oil and plug a line? Sure have.
Heck, I've even seen chowder heads put the vent line from the fuel tank onto the vent tube outlet for the oil tank so that the vaccum from the fuel tank sucked oil out of the oil tank up until the fuel tank vaccum locked and the engine quit running.
But I have never, not once, ever seen an oil injection pump just fail.
Now, if the pump has been properly removed and the oil lines and thier connection points sealed and blocked, you have some other considerations.
50:1 is fine with a high quality, pure synthetic, motorcycle specific two stroke oil, in a liquid cooled engine. If your NOT using a pure synthetic oil, it's way too lean.
Your son's bike is air cooled, but obviously won't be seeing sustained high rpm blasts under extreme engine loads I'd suggest something along the lines of 40:1 (3.2 oz per gal) with a pure synthetic oil. But if your using cheap petroleum based oils, then I'd start off at 32:1 (4.0 oz per gal) and lean out gradually from there until the spooge and smoke clean up some.