Would war service require a machinery refit?

Would surviving Tiger Cubs need major refits or replacement after such intensive wartime use?

Yes: their machinery would probably wear out well before their hulls and need replacement after the war.

Machinery life and hull age diverge sharply in wartime service. A capital ship's wartime year may equal about three peacetime years of use, while destroyers and carriers can approach six because they operate at high speed so often. A fast, widely deployed Tiger Cub falls between those cases at roughly four and a half to five peacetime years for each year of war. Its engines could be effectively twenty years old by 1918 even though the hull is only four, making post-war re-engining or a major refit likely.