By late summer 1918 Germany's position was fairly hopeless. If Wilhelm II had abdicated then, any change in the succession (eg in favour of his grandson), if it was to have a chance of permanence, would have had to be made with an eye to the imminent end of the war. Accordingly it would almost certainly have had to take into account the views not just of the German government, army and people - who were already starting to rebel against the monarchy - but also the allies (Britain, France, Italy, the USA ... Russia etc). I can't see a monarch, whether it be Wilhelm's grandson or another Hohenzollern, successfully sat on the German throne unless it was with the agreement of the, very-soon-to-be victorious countries, and they in turn would have had to accommodate the views of the German people if there was to be any lasting stability.
To my mind any sons or grandsons of Willhelm II would have been seen as far too close to the Kaiser to have been acceptable as either king or regent or even as interim president of a republic. The British might possibly have accepted some remote German princeling - especially if he was closely related to the British royal family and pro-British - but I can't see that the French would ever have entertained the idea. So if Wilhelm II had abdicated in favour of his grandson (and assuming the lad accepted the crown having recently seen his cousins the Tsar and Tsesarevich executed by revolutionaries), I feel the poor boy would barely have had time to get his 12 year-old bum on the throne before he in turn was forced to abdicate, either as a result of revolution or at the demand of the victorious allies, or both. The choice of a possible regent therefore becomes rather irrelevant.
You've obviously read Purdue's work (I haven't) ... so why does he think the Kaiser's grandson would be an acceptable successor?