You will get various amount of advice and always common. Here is what I do but understand that this is only for a day hunt.
1) I prefer early morning and in my usual sitting position before the sun comes up. You can hunt the evening as well but may not find your squirrel, on the ground, if you hunt too late. Sitting by a nut tree is good place to start. Make sure and communicate your shooting lanes.
2) At mid-morning, I start into my stalk, for about an hour or so. Go nice and slow and enjoy.
3) I finish my hunt and clean my squirrels in the woods. I use what they call, the Cherokee method of skinning. U-Tube has lots of videos on this method.
4) I take wash water that I use to rince off the squirrels as well as wash my hands and tools. I then put the squirrels and tools in a plastic bag and into my vest. Game meat does not spoil as quickly as store meat.
5) Just about any small knife will do and I also take a pair of plant clippers that I use to cut off the legs and head.
I know my wife really wants to make this colonial era brunswick stew and if it doesn't turn out right I know for certain she'll feel bad.
Can't hardly go wrong and it's good. I usually just pan fry like chicken and bake for two hours using the old Cambell's cream of chicken recipe, over fresh biscuits. This is making me hungry. Oh yes, greys are better eating but they are all good. .....
Be Safe !!!