Yes

As I said before there is no problem with using the shavings as a
mulch.
The wood will be broken down by bugs and microbes, and they need
nitrogen and they take that out of the air when above ground (air is
something like 80% nitrogen, I think I do remember) not out of the
ground.
It is when it is dug in that it is unable to get at the nitrogen in the
air and it is taken out of the soil by the "buggies" and given back
after they die, but while living and breaking down the wood they are
then competing with the plants.
Also the juglone, a toxic substance that inhibits the growth of many
broadleaf plants (including walnut seedlings) would leach out more
readily in the ground, so composting before adding to the garden is
advisable if there is a lot of walnut in the shavings.

Yes you can use them for a mulch, I have used them for years, keeps the
weeds down and conserves the soil moisture and especially keeps the
soils top layer's temperature from baking the hair roots when the
summer sun shines on it.

You could also mix some in with your other composting material and use
it that way.

I have also a few friends that come to pick some up for mulch and one
that uses it also in his poultry run.

I would not dig it in, in it's raw form, it will compete with the plant
roots for nitrogen to break down, and adding extra might give you other
problems, like to much leaf and no flowers, or spindly growth, just let
it break down above ground naturally.

Have fun and take care
Leo Van Der Loo