Before you cut the GPS cable you must check, that the GPS mouse will provide the correct information (GPS sentence) for the ICOM. It could be that some information will be disabled. After checking and enabeling the correct information (normally with the utility program which comes together with the GPS mouse) you can cut the cable.
Use left and right cable for 5 V power (standard USB pin assignment), one of the other 2 remaining cable is for the jack (the IC7100 will need only one of them). May be you have to check whether cable 2 or 3. No risk for any damage.
Connect the jack with the 71oo and the USB connector with the power adapter and check the correct GPS setting of the 71oo. After few minutes the 71oo must show the GPS information. If not, change cable 2 with cable 3.