Well since you are planning to use a freewheel and not a cassette you likely won't have 9spd spacing between cogs, thus rendering a 9spd shifter useless.
If you really really want to do this I'd get a set of thumbies, either the converters and use TT friction shifters or find a nice set on ebay. You will lose indexing but you will be able to use any freewheel cassette you want, and if you get a nice set (I love my Shimano M700s) you may like them more than a set of nice triggers.
Since you will be using a freewheel you likely won't need to change your derailleurs limit screws just grab yourself a nice vintage 6spd freewheel and a some thumbies and I'd say you'd be rocking.
But wait a minute... you must be mistaken as to what a freewheel is
your Shimano CS-HG50-9
is a cassette not a freewheel... To run 6 speeds you would need to find yourself a 6 speed cassette, or remove 3 cogs from your 9 speed (this can be done by driving the pins in the main cog pack out) and use cassette spacers to fill the rest of your hub (if you keep your current hubs since you won't be able to use a threaded freewheel on your current hubset unless it is a threaded hub, in which case follow my directions above). In this situation you would need some longer limit screws for your derailleur and you would be able to use your current shifters. But if you go with a 6 spd cassette that fills the whole hub body you will need a 6 speed shifter or a friction/thumb shifter.
Hope you get it all worked out and post some pics when you finish!