There are several ways to connect a cut cable. The issues with a depth sounder are basically 2. The length of the cable will alter the depth reading. That should not be your issue as you will reconnect the cable without appreciably changing the length. The issue you need to address is maintaining the characteristic impedance and maintain the shielding. This will affect sensitivity. The Characteristic impedance is related to the diameter of the inner conductor and the distance to other conductors including the shield. That space, the type of material in the middle including air (called a dielectric), and the surface area of the wire actually determine the impedance. You want that impedance to be uniform through the length of the wire (within a certain tolerance). The best way to maintain that is to buy purpose-built connectors or that splice box you referred to. It could, in theory, be done with a soldered connection, but it's not easy.
If I were to attempt it, I'd do this: After routing the cable, slide some additional wire shielding (You could get this from an old coax cable) and some heat shrink tubing over the top and out of the way. Then prepare the wire by stripping a minimal amount of insulation from conductors. I'd want to keep solder to a minimum so as to minimize the lump in conductor thickness. I'd then attempt to keep the spacing between conductors as uniform as possible but re-insulate them. (possibly with heat shrink or liquid coating that would cure.) I'd cover the whole thing with the extra shielding and solder it to the original shield on both ends. Be careful to not melt the underlying insulation. Now cover the outside with heat shrink of your choice of moisture-tight covering. If you're careful, you may be successful. Don't try it if you can't do fine solder work to a high standard. This type of splice should work well at acoustic frequencies, but don't try it for RF frequencies.
Ken