How To Trace The Line Of A Print With The Nozzle (With No Plastic Printed)
Sure. Comment out your E values and the temp set/wait lines:

...
M109 S245
M190 S120
...
G1 X123.113 Y95.644 E12.81357  F250
G1 X125.613 Y94.214 E13.06364 ; skirt
G1 X128.409 Y93.523 E13.31370 ; skirt
G1 X131.287 Y93.624 E13.56377 ; skirt
G1 X133.471 Y94.259 E13.76129     F250 
G1 X133.771 Y94.384 E13.78949 ; skirt
...

Becomes:

...
;M109 S245
;M190 S120
...
G1 X123.113 Y95.644 F250 ; E12.81357 
G1 X125.613 Y94.214 ; E13.06364 ; skirt
G1 X128.409 Y93.523 ; E13.31370 ; skirt
G1 X131.287 Y93.624 ; E13.56377 ; skirt
G1 X133.471 Y94.259 ; E13.76129     F250 
G1 X133.771 Y94.384 ; E13.78949 ; skirt
...

Now the printer won't wait for any temperatures, and won't dispense any material.