Prior to getting into the fluke jigging thing in a big way, whole squid fished on a tandem rig was one of my favorite methods for hunting down the larger fish that we can see here on the South Shore. I make up my own rig with a 4/0 Gami Octopus snelled on the end of a 36" leader (50lb test leader material NOT mono fishing line, which is too limp, IMO). Next, I snell a 4/0 Octopus to the main leader in such a way that its actually snelled around the main line. This permits me to slide that second hook fwd or back to the proper position - depending on the size of the squid I've selected for bait.
What I do then is to take the squid and strip off the two wings and throw them overboard. Leaving them on will do nothing for you except make the bait spin on the leader as its pulled through the water. This wing-tossing can also have an occasional excellent side result as a couple of times we had a nice Mahi come under the boat and eat those wings as we tossed them overboard. A quick flip with a GULP! shrimp-tipped bucktail by my alert fishin' buddy put those beautiful fish right in the fish box.
Anyway, I then take the bottom hook of the rig and drive it into the squid's head, dead-nuts right between the eyes. Next the sliding hook gets positioned up on the leader such that the barb will go right thru the foremost tip of the mantle, about 1/3" from the tip itself. It is hyper-critical that space between the two hooks is properly set by the positioning of sliding hook, otherwise the squid will spin in the water and not catch a thing. The squid MUST lay straight against the leader. If there's the slightest curve to the squid's body it will completely twist up your leader and make a major mess for you to untangle at the end of a strangely unproductive drift. When you get the rig into the boat you will see exactly why you had no takers on that last drift.
If you feel that such a rig is not something that you can tie properly, then there are commercially available versions like the Owner "Boa" that will do perfectly well for you.
I have to believe though that one good reason to read this board is to better hone your personal fishing skills. And learning the terminal tackle side of things is one of the more enjoyable sides to this knowledge search. For me at least there's little in the hobby that gives me more satisfaction than mastering a new rigging technique, and then applying it in a manner that puts some nice fish in the box. So I would encourage you to learn how to make up this sliding rig.
Here's the key point - when you chinch that sliding hook's snell snug, don't make it so tight that you can't move the hook up and down the main leader. The key to this rig is applying just the right amount of tension to that sliding hook's snell such that it can be adjusted fairly easily, yet still holds tight enough to the main leader that it pulls the squid straight thru the water. Takes a bit of practice to get it just right, but once you learn it, it stays with you forever. No worse than tying an improved blood knot, just different.
As far as what to do with squid that get mangled by short strikes or dogfish attacks - I save those mantles and strip them out for use on another rod that I fish on the opposite (Or up-tide side) of the boat - fished dead-stick style out of an angled side-rigger type rod holder. On that setup - typically a reel in the Calcutta 400/Abu 6500 class, mounted on a fairly stout rod - the Daiwa Proteus PRSS64HB comes to mind. I have a B/S rig set up with a super-heavy sinker (Think 10 to 16oz to to hold that rig close to vertical relative to the boat, so that the delicate braid doesn't rub on the boat's bottom) and large teaser or big 6" GULP jigging grub with a long, thin strip of that damaged squid on it.
Its a cool thing to see that rod get hit and take a deep bend as a large fluke realizes that he just made the mistake of his life. Probably the last one he's gonna get a chance to make, if I play my cards right.
Now if your whole squid had gotten mangled in its mid-section, such that the head and tentacles are still intact, that's still something of a bonus. Use that head on the teaser. Big fluke think of a squid head tipped teaser like I think of a fresh, warm Krispie Kreme "Original" - it just won't last very long.
Oh, one last thing - for this specific technique I greatly prefer the frozen West Coast squids that are sold frozen in 3lb bricks. Exactly the right size for this fishing and unlike 90% of the fresh local stuff that the better fish markets sell for human consumption, the heads of the Pacific squids are typically still tight in the body, not falling out of them. I hate that and find loose heads counterproductive to my efforts. For fishing on a sliding snell rig, this makes a huge difference.