No worries - their *flesh* doesn't stain from the ink...once you remove their innards, eyes, beak and gladius (what I call their plastic spine)....it's all good.
I like head(s) **oops>, so I normally cut the tentacles as close to the beak as possible without engaging the beak...you should be able to keep all the tentacles together without clipping the beak. I don't keep the part that houses the eyes either...if you puncture the eyes, they'll bleed goo-ee ink-like fluid. They also tend to squirt most of their ink as they exit the water...(that's where you can have fun with the people on the side of you).
I also don't do their wings, different texture from the body...more of a cartilage-like feel.
*** Any ink you can salvage can be sold to Staples for ink cartridge refills. "That was EASY!"...
Happy /Squidding....it won't last forever!!!