FT-857D Loud TX/RX Relay Click

Here is a recording I just made of the difference between my FT-857D's TX/RX relay and my TS-2000's TX/RX relay. The reason I bring this up is I take my FT-857D on backpacking trips and operate portable CW. However, I like to operate as I am sitting in bed just before I go to sleep - when everyone else is doing the same. I can put head phones on to keep the CW in my head only, but I can't put headphones on the TX/RX relay:

FT-857D vs. TS-2000 Relays.mp3

Note the first part of the TS-2000 recording was actually my key clicking. So I was careful after the first couple clicks to push it softly so only the relay was heard. You may have to turn the volume up and listen carefully - but you can hear it. The FT-857D, in contrast, is very obvious! (and the fans... those are another issue, but I can work with them pretty easy)

Both recordings were made with the recorder about 2.5' away in the shack and both radios were right next to each other.

If any of you have any ideas for quieting down the relay - maybe replacing it with one that doesn't make much noise? Or a transistor? - let me know! It is annoying when everyone is quiet in camp.