Before setting the trap drill a hole in one corner and attach a piece of wire or chain. They can hightail away with trap in tow if they don't get a good whack.

I do that when I use traps.. just a length of Mig welding wire

Yep!!

UPDATE :

Today I got up above the drop ceiling, using 2 ladders & prop rod.
When the shop was built, they made some 3" holes next to every truss to vent into the ridge cap.
While the cap/roof gaps are maybe an inch tops, apparently that's been enough.
I could see a trail of peanut shells & insulation running down from those holes to the drop ceiling.
So, I stapled some wire mesh over each hole.

Seems almost silly now, but man, squirrels sure can squeeze into tight spaces !

if they have a nest in there, that won't stop them.
like I said mine chewed through aluminum siding.

Like I said.. antifreeze

my "little buddy" chewed through stainless steel screen to get in the window i left open a crack for ventilation.
a box trap and a tiny "bang stick" fixed the problem........

And,95 % of squirrel problems are with red's,not gray.

^^^^^ a resounding YES !

Update #2 :

In today's episode of As The Squirrel Turns...

Yesterday bought a Havaheart trap, got some peanut butter, and in less than an hour I had a caged grey squirrel.
Took little Rocket J for a few miles of road trip and let him off in a forested area.
Reset the trap for the next contestant but haven't heard a peep up there yet.

Sounds familiar lol