I am a living historian, part of a group that now portrays the 7th Battalion Argylls in WWII. We rebadged from the 2d Battalion last summer.

For a reasonably full accounting of the disposition of the various battalions after WWI up to the late 1990's, I would refer you to "Fighting Highlanders! The History of the Argyll & Sutherland Highlanders" by P.J.R. Mileham. Your original post asked in particular about the disposition of the 4th battalion. Mileham states at page 106: "At the end of the war [WWI] the Regiment shrank to its pre-war size. All the Service battalions of the Argylls were disbanded, while the 3rd and 4th Special Reserve battalions were amalgamated and placed in suspended animation, until their final deletion from the Order of Battle in 1953. Of the Territorial Battalions, 5th and 6th Argylls from Renfrew amalgamated in 1922 (to be separated again later), while 7th, 8th and 9th continued in service between the wars, until they were required once more at a time of crisis."

In subsequent chapters, Mileham gives greater detail about the disposition and movements of the various battalions of the regiment during and after the war. Mileham was a Major in the Royal Tank Regiment, and his history is one of the best general narratives treating A&SH history. Of course, official histories were published of the Argyll Battalions after the war. Official histories were published of the 1st, 2nd [Malayan], 2nd Reconstituted, 5th, 6th, 7th, 8th and 9th Battalions, all by publisher Thomas Nelson and Sons, Ltd, beginning in 1949.

I hope this assists you in your quest. Cheers!