No Navies? Lets try no armies instead...
In WW1, much grief was wrought by armies. Sure, it might have gotten a bit triggered due to naval races, but said shenanigans paled compared to the battle Verdun or other places on land at the time.
In comparison to human toll with the land armies, the at sea toll was a drop in the bucket figuratively speaking.
My alternative is simple: Limit army sizes to what is absolutely needed for a given country and curtail capital ship construction to the tune of one every two years from government yards only.
The ideal would be to completely axe capital ship construction entirely and let nations focus on Cruisers of Maximum 8"/203mm/20.3cm size for guns while limiting to a maximum of 15,000 tons.
The result in general would be that everyone feels moderately safe and secure and no one feels too bent out of shape about things, except the big ship enthusiasts.
Barring the idea of cruisers and below allowed, and accepting that capital ships somehow needed to be in the equation; I would suggest the above as a way to go about doing it. This would allow dockyards to have some big ship industry continuing, therefore saving parts of infrastructure for ship building.
OTL, Britain suffered a bit getting yards back online because of the outright stoppage of ship construction; which also includes things like high grade engines, boilers and big guns.
With this option I've presented, countries continue to be able to build new ships, but at a slowed rate. Keeps the industry structure there and in place, but not the production rate. Also encourages nations to retain a few ship yards as national yards.
Any ship older than 20 years would be recycled/scrapped unless it is of special mention [aka museumized].
HMS Dreadnaught [First of type]
Mikasa [Tsushima]
USS South Carolina [first superfiring]
As examples.
Yes, I realize that most nations at the time were not necessarily all that forward thinking and were looking at the here and now, but my thinking is that museumizing those two ships that did not get that OTL would be a good thing a few generations down the road.
In the case of the British, a backroom deal would be done to make certain that the RN could afford to museumize Dreadnaught.
Basically, the tldr here is that by focusing most of the limitations onto the army sizes and army tech, most of the nations come away far happier being able to build cruisers to their preference.
Besides, Cruisers and destroyers are the main workhorses of any navy
If none of the treaty powers had any navies, I don't think there would even be a treaty.
Britain relies too much on global trade as does Japan; both those countries would like walk out before accepting a full no navy treaty.
Focusing on tonnage and gun size limit, allow cruisers and the like. Limit capital ships to 1 every two years, allowing the industry to retain some capacity.
Formalize the "qualitative race" to a hard limit of 18". RN was going up in gun size 1.5" for the US/Japan's 2" increments.
US: 12"!
RN: 13.5"!
US/IJN: 14"!
RN: 15"!
US/IJN: 16"!
RN: 16.5"! [Secret 18" work...]
US/IJN: 18", final offer.
RN: Done!
I fully expect to see a lot of discussion and references to previous threads on this subject.
My overall point is that armies kill each other far more impactfully than ships; but because of the value factor with the ships, prestige is given to the naval side while the army issue tend to be kept under the rug. Therefore, one should impose greater limits on armies operating than navies, because armies have great impact on the land.
And I'll let others play the numbers game with the fleets.