Repairing rot in window framing
If this wall is parallel to the trusses, it is probably not load bearing. At least that would be typical.

Water infiltration

You must address the cause of the water infiltration, or this will only happen again. 

You noted the lack of housewrap, and that may be contributing, but since its by the window I'd say correct window flashing is essential. Check with the  window manufacturer for instructions (they are all similar but for example: Andersen). The details really count, especially how to lap one layer over another, etc.

If you can do it from the exterior, I'd also air-seal the window to the framing while you have the chance. (e.g., Canned spray foam - low expansion).

You should add housewrap (or tar paper) wherever sheathing is exposed, and if you ever re-side tie into that later. 

Framing

This is a reasonable repair to do yourself. It sounds like the rotted studs are possibly still adequate. i.e., if they are solid the remaining thickness and no water has reached the interior, you might be able to just live with them as long as the wall is closed up correctly. 

You could also sister new wood side-by-side with the existing which would avoid tearing out material and damaging the interior finish. The key thing is that the header is still supported by the left stud. If you sister the king stud there you might run some long structural screws (like Headloks) just to ensure the new wood will support the header.

The thing that concerns me most if you want to leave the damaged wood in place is the sill plate. If that is rotted through it isn't doing its job (transferring the load of the wall, ensuring shear transfer through the sheathing, etc.) However you could probably just cut out that rotten piece and slip a new one in. This is unlikely to damage the interior since it is probably behind trimwork. You could also leave the rotted section if its small enough, and slip in 2 or more 2x4s on the horizontal over the top of it. This might spread out the load adequately.