How hard is it to replace a section of copper pipe

A few months back I had a small leak under the kitchen sink. Traced it to the water filter. The city cut the water off for a few hours to connect the new subdivision being built across the street to the water main. When they turned it back on I think the pressure loosened something.

All has been fine since then. I think that was January. Today my wife tells me it's leaking again and sent me a pic. I don't think it is the filter this time. I'm looking at replacing a short section of pipe and two hose type connections. It is old copper from the late 60s. Is my best bet getting a copper to pex conversion and running that straight to under the sink and adding shutoffs there? I'd like to replace hot and cold while I'm at it. I have easy access from the basement below.