You could try something like this:

alphaKWith2 = Outer[DisplayForm@*FractionBox, alphaTESTwith, kappa]

This is in a different order than your final table shows, so you would dispense with one Transpose:

gridWith2 = 
 Grid[Insert[Transpose[Insert[alphaKWith2, N@particleclass, 1]], 
   Prepend[N@particleclass, "Table"], 1], Frame -> All]

Now, I'm still not sure if this is quite what you want. Maybe you want all numerators to be in scientific notation:

alphaKWith2 = 
 Outer[DisplayForm@*FractionBox, ScientificForm /@ alphaTESTwith, 
  kappa]

But anyway, hopefully this points you in a useful direction.

Sorry for the lack of clarity. What I mean is that I wanted it to not evaluate the division but display it as a fraction instead.