Since as far as I can tell the Drawing Tools palette always uses the system (e.g. Windows) color picker I don't think it is (presently) possible to solve your first question.
Your second question has more possibility:
Is there a way to change the colours of objects made with Drawing Tools that will allow me to enter the C, M, Y, K values into input fields?
I believe that the functionality on which I shall depend was introduced in version 10.
Let's start with first example from the Graphics
documentation:
gr = Graphics[{Thick, Green, Rectangle[{0, -1}, {2, 1}], Red, Disk[], Blue,
Circle[{2, 0}], Yellow, Polygon[{{2, 0}, {4, 1}, {4, -1}}], Purple, Arrowheads[Large],
Arrow[{{4, 3/2}, {0, 3/2}, {0, 0}}], Black, Dashed, Line[{{-1, 0}, {4, 0}}]}]

Although entered with directives here such a graphic could be constructed using the Drawing Tools.
We can convert this into an editable form by applying Defer
to the head using Operate
, and we can convert all color directives to CMYKColor
type:
Operate[Defer, gr /. c_?ColorQ :> ToColor[c, CMYKColor]]

If we click on any of the color squares we get a CMYK setter like this:

After changing the color and clicking OK we can evaluate the cell to render the new Graphics:

Manipulate[ ListLinePlot[Sin[#] & /@ Range@20, PlotStyle -> {Thick, color}], {color, Gray, ColorSlider}]
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