Spencer,
The faucet in my Westy may well be the original and was difficult to
operate with wet hands and next to impossible to operate with soapy hands.
Not knowing if a new faucet would be any better (five or six years ago),
this product caught my attention:
http://www.gowesty.com/product/faucets-plumbing/4209/hands-free-faucet-
kit-?v=

It's a pneumatically operated switch, the control for which can be placed
anywhere.  I chose to place the control on the front right corner of the
sink counter and it allows me to operate the faucet with the back of my
hand, the forearm, or even my elbow. Sticky, greasy, or soapy hands are no
longer a problem; just bump the control and the faucet comes on, and
another bump and it goes off.  It's less expensive than a new faucet and
the convenience factor is great.