I don't think Wilson was expecting major battles in Latin America the day after the war ended or anything that drastic, certainly the Military and Naval expansion authorised in 1916 had a 5 year schedule for completion. Rather I think that instead of a benign Britain in effect enforcing the Monroe Doctrine the US would have to deal with Germany who might well do similar interventions as the US in support of its business interests, or picking sides during instability and supplying assistance to that side during the 20s.
And how, exactly, are they going to do that when the track record for trans-hemispheric interventions up to that point and even in that period is pretty abysmal without a pre-existing friendly power to operate out of? If the US is genuinely worried about Germany mucking around in the Western Hemisphere it won't take much to keep the Germans on their side of the Atlantic through a combination of diplomatic action, pressure on Latin America (which is much easier for the US to exert in every way) and already having a head start on coupled with far greater capacity for building up a sufficient navy to keep it that way.
You're also ignoring that a victorious Germany is going to be too busy securing Mittleuropa, most likely intervening with mixed or disastrous results in the Russian Civil War, keeping Austria-Hungary from going down the tubes completely and stabilizing their position in Africa. They won't have the time, inclination or resources to do anything regarding the Americans beyond making funny faces at the US and if you've got a situation where the US is staying out of the war that's going to be in part because German foreign policy would be actively seeking to avoid antagonizing America. It's also a very ahistorical assumption to say the US depended on benign British assistance by this point in time to maintain the Monroe Doctrine. That was true during the early to mid 1800s when it really did depend on the Royal Navy to make possible but by the time of the Spanish-American War and the launching of the Great White Fleet the United States was more than capable of doing so without any assistance with no real debate from the rest of the planet.