Susan: sorry to convince you spend money on the connectors.. yes, you are right, it's possible to dismantle.
The drawback is, if you move the phidget around, or bump the wires, there's a good chance they will wiggle out or disconnect. Getting them permanently stuck to the green screw in things is not possible, they will eventually slip. Actually, you can probably hot glue them in place, that'll last for some time, alternatively, put a good chunk of epoxy there, but that will be permanent.
It sounds like you aren't planning on moving the parts much at all, so you should be good. But, in case you don't put any strain relief on the wire, and you do end up with weird results in your logging, file this away in your memory: check the connections of the TC at the phidget. I had many, many hair-pulling encounters early on that were simply the result of a lousy connection.