I don't have such an oil cup on my MZ either, but I have something very similar on a 2T electric generator, in PE.
I always carry a bit of oil with me (in the battery area), just in case, but if I plan to mix at the pump I take a set quantity of oil with me, and fill up with the desired amount of fuel. And then, after I ride away, a bit of acrobatics to mix it. Just to show oil + fuel do need shaking to mix well, this is what happens if you just add the (red) oil to the fuel, without shaking:

- Shake it.jpg (27.9 KiB) Viewed 123 times
Anyway, some more comments:
• I did about 25k miles with my 251 & I measured my oil pump (before I took it off), it did pretty much 1:51 on average. Proper adjustment is very important. And yes, when you have the thing idling while you open the oil pump's control thing, pretty quickly it starts smoking, but that is just because then the pump thinks you're giving full throttle, hence assumes far more fuel is entering the engine too.
But either I could not trust my oil pump (though it always required a consistent quantity of oil, and it never ran dry), or the amount of oil it got, 1:50, was insufficient for my riding style (it gets quite some full throttle). I say this because in the more distant past I lost a small end, and more recently I saw grinding marks on the piston than can only be attributed to insufficient lubrication. And this while I have always used fully synth, or a good semi synth. So I took the pump off & premix 1:33 = 3L oil/ 100L fuel, instead of the recommended 1:50 = 2L oil/ 100L fuel. And now all is well. Quite possibly 1:40 = 2.5L oil/ 100L fuel would work too - but why bother?
• I did not say depending on the application, I said depending on the objectives, and that's exactly what I meant. Objectives & priorities. My objective here is to keep the thing working as well as possible at the lowest possible costs in terms of expenditure & effort. I do not mind if there is a bit of smoke from time to time, though my MZ does not actually smoke visibly, with this oil. (My Jawa does, on full throttle & high revs, and my riding buddy once told me 'I could see you had gone past here, from the puffs of smoke' - hence my name.) But I suspect MZ wanted to achieve a greener & cleaner image, even with all the Trabants & heavy industry, so for them preventing smoke (their oil smoked much more) was a priority, and I suspect that played a role too in their 1:50 recommendation. It should be, as in the end pollution was the demise of the 2T.
So, you see, the objectives & priorities of the mere amateur can differ from those of the manufacturer, and yes, as the owner of my bike I will sail my own course.
• Yes, that is correct: if you take out the pump & go for premix instead, the mixture gets leaner. For (at least) 2 reasons. Firstly, a metered amount of fuel (mix) now only contains 97% of petrol, while the other 3% of semi synth will exit largely un-burnt through the exhaust, hence absorb little oxygen. Secondly, and this is more difficult to quantify, the viscosity of the premix is likely a bit higher than of pure petrol. With the fluid being metered by jets & a set ΔP, the flow will be slightly lower if you were to use the same jet.
So you get less fluid, and the fluid that you get contains only a fraction of petrol --> the mixture gets leaner.
All anticipated, so the jetting was adapted in the process.
• These engines (250cc ETZ's) have been used extensively for racing, particularly in the UK. See
https://www.youtube.com/watch?v=fyXNoMw4ki8.
• Breakwellmz, would you have any pics of your MZ's? I'm particularly interested in the trail bike versions. Ta.
Edit: sorry Blurredman, hadn't seen your latest post. If there's no difference in jetting recommendation in the manuals, that's once again an indication of the dependency of those recommendations... Sail your own course.