First shaving the tires isn't going to get you anywhere, the rubber will be nearly the same below the surface.
I tend to think of rubber as a plate of spaghetti. The noodles are the rubber molecules (except in the tire, they are actually cross linked) and the sauce and chunks of sausage, green pepper, tomatoes, etc., are all different things that are mixed into the matrix. (Who would have thought that talking about tires would make a person hungry??) As the rubber is flexed, these mixed in things are free to migrate, so stuff like oil, waxes - stuff that makes the tire "soft" - evaporates on the surface and gets replaced by what is still imbedded in the rubber matrix. When you get to the point where the rubber properties have changed, this migration has pretty much used up whatever it was that affected that property within the matrix, and not just on the surface.
So if the idea is just to bring back a bit of the grip, you might try using tire traction treatment such as Formula V. Just be aware that you have to take the tires off the car, and it will be at least 24 hours before you can put the car back in service.
But if your goal is get a bit more life out of them - I'm going to suggest that if the rubber has dried out on the surface, the rubber has dried out around the belts - and that means the tire has lost some of its durability - and it would be safer to replace them than to try to "rejuvenate" them. An indicator of where you are in the duarbility part of this is the cracking. If the cracking is superficial, then the tire is probably OK (notice I said probably), but if the cracks are plentiful and or deep - and especially if the cracks are on the tread surface - the part that contacts the road - then it's time to replace the tires.
What do I mean by "Probably OK"? I have seen tires that show very little cracking that have failed - and the common denominator has been age - many of these have been spares as installed at the vehicle assembly plant and becae part of the second set of tires. Cracking is a combination of material properties and flexing. So a tire that hasn't flexed very much, isn't likely to show cracks as readily as a tire that has.