How do I smoothly join endpoints without affecting the rest of the shape?

If you have a specific shape you are working with, please post a screen shot.

UGStudios,

First of all, the Ctrl-Alt-Shift-J will inevitably and irreversibly change the path(s) by moving the end Anchor Point (together) so there is no real way forward from that.

Smart Guides are your friends.

To create a customized curved segment between the end Anchor Points, you may, with everything deselected to start with (click an empty spot on the Artboard/Workspace):

1) For the first Anchor Point, if the last segment is curved, Click it with the Direct Selection Tool, then with the Line (Segment) Tool ClickDrag from the Handle into the end Anchor Point (snapping), otherwise just ClickDrag a suitable distance backwards from the end Anchor Point along the segment; this will create a straight helpline, then give it a different Stroke colour to make it clearly visible;

2) For the second Anchor Point, if the last segment is curved, Click it with the Direct Selection Tool, then with the Line (Segment) Tool ClickDrag from the Handle into the end Anchor Point (snapping), otherwise just ClickDrag a suitable distance backwards from the end Anchor Point along the segment and give it a different Stroke colour to make it clearly visible;

3) ClickDrag the first helpline by the far Anchor Point to snap to the end Anchor Point; now you have tangents for the segments to join;

4) With the Pen Tool ClickDrag a suitable distance from the first end Anchor Point along the first helpline/tangent, then ClickDrag a suitable distance from the second end Anchor Point along the second helpline/tangent; or if suitable you can just Click one of the end Anchor Points and only have a Handle on the other one; the new segment forms an open path with the two helplines;

5) With the Direct Selection Tool click each of the helplines/tangents and press Delete once to remove them; this will leave you with an independent curved path between the end Anchor Points; you may click the path and adjust the Handle(s) until the shape looks right;

6) Deselect and ClickDrag over each end Anchor Point (set) and Ctrl+J, select Corner if asked to preserve the proporties of the original last segment.

Try using the curvature tool.

I don't believe there's a way to auto-calculate the curvature of the join. But, once you've made your join you have a few options to curve that point.

1. You can use the direct select tool to select the newly joined anchor point, and you'll see a blue dot appear below/outside of the corner-joint. Click on that and drag and it'll round the corner for you.

2. If using a heavier stroke you'll see you can change the stroke value to have a rounded miter instead of a sharp miter. That's in the stroke panel as an option.

3. You can use the Effects to Stylize > Round Corners.

There are other options too, but all of them will be produced after the corner is joined and not done automatically.