How to set up tap/faucet for cold water only?
Three ideas off the top of my head:


Terminate the end of the disconnected pipe with a valve. You can mitigate legionnaire's risk with a maintenance plan to open the valve in order flush the disconnected pipe every month or so. (More research needed on required frequency of flush through if you do choose this option). I'm against this option because of the maintenance: it's ongoing effort, you may forget it and not do it as frequently as required, if/when you sell this house it's almost certain that you'd forget to tell the next owner and/or they wouldn't take the maintenance requirement seriously.
Branch the cold pipe, and feed one branch into the cold inlet pipe and one into the hot inlet pipe.
Buy a replacement tap which only expects feed from one pipe. This may be problematic, as I think most non-mixer taps are designed for smaller mounting holes than mixer taps are.




Option 2 seems to be the winner as the others don't seem overly practical.