Running nicely-that sounds a very healthy PeeWee! . I do use afterrun oil (but nowhere as often and as regularly as I should!)-if your fuel contains castor then it is probably a good idea-but ideally you'd want to put a couple of drops down the air intake of the Pee Wee-the reason being the reed valve seating-the big bugbear with all the Cox reed valves-not just the PeeWee-is that the residue from castor fuel is very sticky-and will 'glue' the reed in place on its seat if the motor is allowed to sit around after running. [I'm talking weeks or months here-I doubt it will be an issue after only a few days-such as one weekend to the next] Result-the engine won't run next time-runs out the prime then stops. Afterrun oils usually have detergent and penetrative additives to help get in all the nooks and crannies-so certainly help in this situation. If you're not running castor then its not really an issue-but most of us prefer castor for the sake of the little end ball joint. If your background is R/C cars then you'll be used to low oil, medium nitro synthetic oil based fuels-which while admirable for their intended use, are less than ideal for Coxes.
So if you're going to run it again in a few days, I wouldn't worry-but if its going to be several weeks or longer before it gets used again, then by all means introduce it to some AR oil.....
ChrisM
'ffkiwi'
PS The TD 010s and 020s can be just as frustrating in use-even though they don't use reed valves-in their case it's the 3 tiny jet holes in the venturi, plus the feed hole in the needle valve banjo that block up with fuel residue....