Why would you want to leave out GITC or GC from the binding buffer ? These contribute to eliminating contaminants such as proteins, and, as pointed by Laurence, they are required for binding the DNA to the solid phase. If your worry is contamination of the eluted DNA by residual GITC or GC, you can include an additional washing step with the ethanol-containing wash buffer, as well as wiping the outside of the mini column before proceeding to elution
I agree with the above answers that chaotrophic salts are essential in column purifications but would add that historically DNA in gel slices could be dissolved in sodium iodide and bound to glass beads and then washed and eluted if NaI is any better for your downstream experiments than GITC or GC but Pierre Béguin suggestion of an extra wash ( or two) seems very sensible