I've done this with my FT-857. Works fine.
What I've found works best for PSK and CW is to work "split" where you receive on one VFO in CW mode (to get the narrow filtering) and transmit on the other VFO in USB so you can use the tones from your software (HRD, for ex.). When the radio is in SPLit operation, it works automatically.
To do this, you need to tune the radio in CW mode until you get a good signal. On the 857, the purple light lights up.
Push the A=B button to match that in the other VFO
Push the A/B button to switch VFOs and select SSB in that VFO. That will be your TX VFO.
Push the A/B button to switch back to the VFO in CW. That is your RX VFO.
Finally make sure your software is set to send tones on the same freq as your CW TONE (I use 800Hz, but you can adjust it to whatever you like. The important point is that your software is set to the same tone).
Just remember, that if you retune your RX VFO to go to another station, you need to repeat these steps.
Also, when you're done, don't forget to turn off the SPLit feature (Don't ask me how I know that
In this configuration, you can listen (and decode) using the narrow CW filters to help your software and your ear, but transmit using the SSB mode. The way the radio is set up, if you are listening to a frequency in CW, the radio shifts the "base" frequency by the value of the CW TONE setting. So, if you set your software to send tones on the same freq (800 Hz for example) as the CW TONE, when you switch to USB, that will result in transmitting a CW carrier on the freq. you were listening to.
It sounds more confusing than it is in practice because the radios (at least the Yaesu radios) are set up so that it just works. I've done this for PSK a lot and "Signalink CW" a few times.