I think what you are talking about will work. Another option is go to a scrap yard and get a section of hose. Cut the tubing about two inches from the end of the hose. Get two copper connectors with crimp fittings on each end I think 5/16 inch this will attach the hose. I've seen people buy a copper crimp elbow and use it when cutting a hole in the bed of a pickup they cut the line. You can also buy goodyear hose rated for a 100psi for fuel line. It also has a plastic insert.
Did you break the line or is the connector itself leaking. The copper fittings you can get at the hardware.