The family tire-shop has been buying some flavor of GREEN Go-Jo that comes in a plastic bladder that fits in a dispenser on the wall.
I commandeer a box every once in a while, sort of the ox not being muzzled, or maybe a perk.
Anyways, I clip off a corner of the bladder and squish the contents through a funnel and into a jug.
I keep a squirt-top bottle of it sitting by the sink.
It works well all by itself, with no water whatsoever, but it really works good when used with water, both while washing and for rinsing.
It has lots of grit in it.
Now, the best way to get clean is to keep clean.
There are a few tricks for that.
A FUMOTO drain-valve and oil-filter relocation kit works wonders.
I wear cowhide leather gloves almost every waking hour; I keep a few pairs of the filthier ones on hand for when I am handling such things as greasy hubs and such.
I may switch back and forth between the cleaner gloves and the dirtier ones twenty times during a project.
Being in the habit of always wearing good gloves (I use the "ROPER" gloves from Harbor Freight), I don't have most of the usual problems that most do with dirty hands.
I can answer a phone, open a refrigerator (and drink), take a leak, or open a door WITH CLEAN HANDS at almost any time.
I have worn gloves so much that I find myself putting them on for such tedious jobs as tying on a fish-hook or threading a needle; I just have a better feel with the gloves on.
If what you are working on is gonna be greasy/oily, slather plenty of vaseline all up your arms and all over your hands, smashing a goodly amount up under the nails.
Pre-treated thus, any grit and grime will simply wipe away.
Oh, and don't try to open any doors while your hands are all slicked up; might wanna take a leak first also.
Digging your nails into plain old bar soap prior to work will prevent anything else getting under there.
When it is the arms that are gonna get filthy, take a pair of old over-the-calf socks, cut a thumb and fingers hole in the toe, and sleeve the arms with these old socks; when done, simply discard the socks.
Old *****-hose also works for the above trick.
A few minutes with a pressure-washer and good degreaser applied to whatever area is gonna be worked on will make certain that the only black you get on you will be from inside whatever it is being worked on, and not a bunch of gritty grimy filth that you just happen to rub against under there.
The product name slips my memory, but there is a product that you rub all over the hands/arms and let it dry into a second layer of skin if you will.
When the job is done, this film peels away like a sunburn and the dirt goes with it.