Treaty-free navies would build their own Tiger Cub cruisers

Would Tiger Cub-style cruisers be built by other navies in the 1930s without treaties banning them?

Yes; the type would likely spread, but navies would build their own national versions.

Tiger Cub-style cruisers would probably be built in a 1930s world without treaty restrictions. One universal export class is less likely. Individual navies would translate the broad concept into designs suited to their own requirements and yards. A compelling type can spread internationally while remaining nationally distinct.