Solder directly to the pads on the LED tape. Extend with CL2 cable as necessary (this assumes it is low voltage tape, and not some of the wonky 120V tape that's out there). You can heatshrink the connection if you wish, but it's not really necessary.
The shop I work for builds light boxes, and we use (literally) several miles of LED tape per year for various projects. All we do is solder to the tape; it's faster, cleaner looking, and the connectors have never held up well over time in our experience.
Use a good ELECTRONICS GRADE rosin core solder and a high quality (preferably temp-controlled) soldering iron. Clean your tip with a wet sponge regularly. Tin the pads on the tape, tin the end of the wires, and tack-solder the wire to the tape. Practice on some scrap tape until you feel comfortable; it's easy to ruin the pads with too much heat. 18ga wire is about the largest size you can successfully solder to the tape. We usually use leaders of 20ga, and transition to 18ga (or larger for voltage drop compensation) right next to the tape using "Eurostrip" terminal blocks.
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