First, if its a 3-screw (no screw in the front of the triggerguard) then its much later. The triggerguard screw was dropped from K frames in 1961. If by '3-screw sideplate' you mean it has the upper sideplate screw then it predates 1955.
If it has no upper sideplate screw but _does_ have the triggerguard screw (4-screw) and no model number in the crane cutout then it dates from between 1955 and 1958.
Prior to 1948 there were a number of minor changes that might be of interest to advanced collectors.
Values for a 1946-1958 K-22, in the latest edition of the Standard Handbook of Smith & Wesson, lists $600 in EXC condition and $425 in VG. At 85-90% you're in between those.
That said, be aware that prices on older S&W's in nice shape have been _insane_ lately, and highly variable depending on the motivation of the buyer and/or seller. While there's no mention of differing value in the book, in general 5-screw guns demand a slight premium over 4-screw.
After 1958 they were stamped with the model and dash numbers and worth somewhat less (but still fine shooters!)
Not trying to be pedantic on the screw numbers, but its important we all be on the same page; they do affect value.