Where is the modification of an aircraft from floats to wheels and vice versa logged?
If the aircraft was type certified in either configuration, then no STC is necessary. Technically there should be an entry in the logbook for a landing gear configuration change, because it's considered maintenance and all maintenance is supposed to be recorded. Unless the aircraft is registered as "experimental" then the pilot is not allowed to perform anything more than Elementary Maintenance as defined by the regulations.

In Canada you don't need to reference the section of the AMM you performed the work to, they just make it mandatory to make reference to any work performed in accordance with another standard, such as an STC or a component maintenance manual. I've worked in four other countries and they had the same rule regarding the entry of maintenance, but I couldn't say for sure if it was the same way everywhere.