For Britain, at least, no WT would probably be quite handy economically. The naval construction freeze had a fairly substantial impact, as it put up enemployment as unneeded workers were laid off, and it dried up orders for materials, which caused steel mills and the like to lay off workers, which in turn caused a reduction in demand for ores and coal and caused those businesses to lay off workers. Keep the government contracts coming, and it's all much cheerier. Additionally, as I said above, the RN was committed to a policy of retiring vessels after a period and replacing them with new construction on a class-by-class basis.
Overall numbers would probably tend to decline, but given the dizzying heights of naval power that the RN had just experienced, even normal peacetime was a dramatic reduction. I recall reading that the British were not as bankrupt as is commonly assumed in the interwar period, and given that this building could be sold to the public as a replacement program rather than an expansion, I could see the British getting away with new BB construction. The RN also identified a need for a commerce protection cruiser during WW1, so they'd probably get stuck into building a few of those too - troubles in China, the Russian Civil War and the demands of the Empire would IMO give sufficient impetus to get those through, and unlike battleships, cruisers aren't seen as an inherently warlike ship.
The British are the only major naval power I can really see getting involved in significant naval construction in the early to mid 20s. The Japanese will have a solid crack at the 8-8, but after Kanto they were stuffed. The Italians and French mostly compete with each other, and already have a rough parity, plus neither has a significant amount of national pride wrapped up in the navy.
The US has an absolute glut of battleships, and IMO the USN would have a very hard time selling Congress on new construction without a war or an obvious sign of weakness or obsolescence on the part of the existing fleet. Additionally, IMO the USN would try to get as much new construction money as possibly poured into creating a more balanced fleet.