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When using punch down tools, you should not have to strip the individual wires.
If you are using the CAT5e run for network connectivity, you might run into connection stability trouble when not using the right connectors. With that said, a Fast Ethernet (100 mbit) only uses 4 of the 8 wires, so you could in theory connect them with a terminal strip, or even an old phone wall jack, which usually has several screws. If this is for something else (i.e., sensors, serial connectivity etc), then you can you could even use small wire nuts.