5w40, 10w40, 15w40 all would work just fine. All are 40w oils, and regarding any warranty concerns, no dealer on the planet can tell the difference between 40w oils. the only difference is the cold flow rating and will not show up in oil testing, especially so in used oil testing. 5w40 does covers all the extremes if one wants a one size fits all oil, but that is limited to full synthetic only, with the associated higher cost. In most of my diesels, I use a 15w40 in warm months and 10w30 in cold months. Both oils in a syn blend formulation and competitively priced to even conventional oils. I am not a real fan of a 0w40, primarily because the base oil is about 25w and it has to use a ton of viscosity index improving polymers to meet a 40w viscosity. Unless one is starting cold engines in some very blistering extreme cold temperatures, I would just avoid it.
And has been stated, CK-4 is backward compatible to CJ-4, CI-4+, and CI-4. I have been using a CK-4 for over a year in a 2000 year Detroit engine and used oil analysis shows it is equal with CJ-4 in protection and wear numbers. That engine is on its 5th oil change of CK-4 this year and runs for roughly 450 hrs per oil change.