the capping sounds a bit like what was there before ( although poorly executed). I think if we do that we will run it flush with the stringer so that it looks cleaner.
The only issue with doing that is that you'll end up with a visible crack line which may vary in size as it goes up the stairs. That's why I suggested a slight set back to form a quirk (it's a long standing way to deal with this sort of issue and make the join less obvious). It also allows you to potentially buy an off the shelf timber strip as opposed to having to have a strip machined to size. Another way is to have a capping the same with as yoursuggested method, but to incorporate a small rebaye along the bottom edge. This can be DIYed, but it does require woodworking tools
This is a rough sketch of what you have to start with (the lower image shows the gap between the wall and the back of the stringer:
First thing to do is to trim out the last 10mm of the skirting. Whilst this can be done with a hand saw and a straight edge, it is far easier and you are a lot less likely to damage the wall if you use a multitool and straight edge. The straight edge needs to be attached temporarily to the skirting to do this job and I'd recommend taking the bottom bit (the cover bead for the laminate expansion gap) before commencing. It can be cut to length and refixed later. You should end up with something like this:
The two techniques I was referring to above are the set back style:
and the rebated style:
The problems are that (i) to do this type of capping you'll need at least an adjustable mitre box or possibly a powered mitre saw and (ii) you didn't mention this in your previous post:
Part of the problem is the curved bits of the stringer...
which does change things quite a bit! Any chance of a photo which shows these curved bits?
what about fake posts at the top of the stairs so that the stringer and the skirting boards don’t have to connect? That seems more within my skill level.
Yes, and you can actually buy what are called half newel posts for this purpose, but you'll still need to trim away the original skirting to get one of those in and you are tight enough on the right side of the stairs but appear to have absolutely no space at all on the left side, so I think the backs of the half newels would need to be notched out so that they could sit over the tops of the stringers