a standard coax can be spliced, but it takes special tools to keep the sheilding intact and working properly. You can get the combo tool at Radio Shack If I remember, the coax on a gps is smaller in diameter than your run of the mill TV coax, so would require a smaller tool. Don't know where you would get that.
Like all home DIY's I 've installed vast amounts of lengths and runs of coaxials.
If I have an issue with one, or forget which one goes where, I do the 9v battery test. Remove each end of the cable from what electronis they are plugged into and hook 9v+ to center solid wire and neg to outer grounding sheith/wire.
Go to the other end with your voltage tester. If it shows 9v then you probably don't have a cable issue.
9 out of 10 times problems with any wires is usally at the mounting point. Even if the connector looks good, it may not be. Especially with coax.