if there is lot of protein availiable use ITC if not but you got Tyr or Trp in the binding site you could use fluorescence titration experiment. both can be used for Ks determination. For specific interction (H-bonds, etc) you will need NMR X-ray crystallography, CD.
Is there any biphysical methods available that can be used to determine the interaction, without involving any type of crystallization step and involvement of tagging??
Yes, you can use ITC. It is label free and a solution method and gives H, S, affinity and stoichiometry values in one single experiment. Only downside is you may need more protein than say a fluorescence based method.
If you are working with purified proteins, above mentioned biophysical methods probe the physical interaction. You can also add SPR and Analytical ultracentrifuge to the list.