I use MultiCX on a Workbench 2/3 setup:
http://aminet.net/package/util/cdity/mcx256This is a very useful little commodity, which includes an anti-click.
Read the documentation though about the anti-click feature because depending on your particular floppy drive, you may have to adjust a setting (tooltype) to get the 'click' to totally disappear. I had to do this on mine (10 years ago).
What happened with mine is that the anti-click feature only half got rid of the click (as in your case)...so I read the docs and there it was, some adjustment in a tooltype - I got the click to go ENTIRELY. :rtfm: