Just checked on the R/H 4700 shifter and it, and the Shimano website, says 10 speed. Why do you say there could be problems using 4700 on a 10 speed?
4600 tiagra is 10 speed and the shifter and RD work on same pull ratio's as "old school" 105 and Ulegra / DA 10 speed i.e, same as shimnao 10 speed MTB series.
4700 tiagra is also 10 speed but the shifer and RD work on a different pull ratio to 4600 et al, the same pull ratio as all shimano road 11 speed series. At bit ridiculous, but I guess they could use some of the 11 speed internals in the shifter but with 1 less click.
This is also a pain if your old 10 speed 105 etc shifter or RD breaks as there isnt a "new" replacement, you are left scouring
ebay for used or finding some dusty old stock somewhere.
For what you are attempting, you probably need to just find a MTB / flat bar shifter & deraiieur set, the cassette and chainset you can reuse and then make sure you choose compatible brake levers