[RPG] How much information should I impart to the players for starting Storm King’s Thunder

The books are designed to let the DM choose how to connect them. There is no 'you must play XYZ book before ZYX book' ordering, except insofar as levels restrict. (It would make no sense to finish Rise of Tiamat then jump into Curse of Strahd, for example, since COS ends at a lower level).

While SKT is written with the assumption that HotDQ/RoT has already occurred, there are even notes inside it on how to invert that paradigm if desired.

Either will work fine.

First, I hope it's obvious that creating L4 second PCs for each player and starting during chapter 2 poses neither narrative nor mechanical problems--it's basically exactly what's intended.

As for starting at chapter 1 with new first-level characters, Storm King's Thunder is designed to start with a full party at level 1. At worst case you'll have two L5 and two L1 PCs; the 5s will grossly outpower the 1s, allowing you to breeze through encounters pretty quickly. But Those L5s will be gaining little 25XP and 50XP increments, which won't do much for them; the L1s will be L3 within a couple of days and, for the rest of the campaign, will alternate between lagging by one level or being at the same level. (The XP progression has you in mind! Your second set of PCs may even be 4th level before the first set hits level 5--look closely at the XP chart on PHB15.)

That said, I advise starting the two new PCs at L1.

If I recall correctly, your two players are relatively new to the game. Managing two PCs isn't a crazy task, but using the first few levels as designed--to teach them the abilities of that PC--is going to be a useful construct. (See "Tiers of Play," PHB 15)