I believe that some string companies make special E-C tuned sets, but I imagine an easier and method that would give you far more choices would be to purchase a 4-string set as well as a single high C (if your local store doesn't stock single strings, JustStrings.om carries a huge selection). As for changing strings, I've always taken whole sets off so I can give my Rosewood/Pau Ferro fretboards/non-finished fretboards a good cleaning of the wood and tuners/bridge and oiling of the wood (Maple only gets a cleaning) before restringing - modern basses with multiple piece necks, strong truss rods, and Graphite Reinforcement can certainly stand the 20 minutes unstrung for a good cleaning and oiling.
The only issue you'll likely run into is needing a new nut, as now you'll have an E-string rattling around in the slot cut for a B and so on down the line, and possibly a setup due to the change in tension substituting a high C for a low B (an increase in tension, as it takes more to tune the C to pitch then it does the B) - unless you have a good amount of experience in these areas I'd spend the money on a quality setup.