From the data sheet, it looks as if the MAX 4619 is of similar construction to 4000 series CMOS analogue transmission gates like the 4066 or 4051/52. If that is so it is very difficult to eliminate all the switch clicks. Slowing down the 'gate' turn on time is not an option with this type of analogue switch. The attached jpeg, from a very old National audio data handbook, shows some of the detail of the FET alternatives - and describes the transmission gate limitation.
Having said that, it is possible to get pretty close to silent switching from these ordinary analogue switches, if you follow KMoffett's suggestion of maintaining a fixed DC high resistance 'half' rail' bias, on both sides of the switch - and capacitively couple the signal in and out
The other problem you have, from the diagrams you have posted, is that it appears that you are switching the output from the pickup directly into the analogue switch. I'm guessing there's quite a lot of gain after that, and even with the DC bias problem dealt with, the remaning switch 'clicks' are going to be magnified --probably to an unacceptable level.
Ideally, you need to do the switching after the pickup gain stage -it's going to be very difficult (if not impossible) to get rid of the switch clicks otherwise.