Hmm, - - that's a tough one.
For ease of explanation, - - let's discuss it like you were replacing the corner post only.
I don't know how many fancy tools you own, - - so let's just go with a pair of snips.
Start snipping upward from the bottom of your corner post, - - about 1/2" in from the outside edge of the corner (either side), - - snip it all the way up to the top, - - now your corner is still attached, but it is two separate pieces.
Starting from the bottom again, - - and the larger of the now two pieces, - - and gently pry out the post flange and nails, working your way all the way up, - - then do the same with the remaining partial post. You should have enough play in the siding itself, - - because it won't normally be nailed to close to the ends (plus it's nice warm weather).
Now take two lengths of scrap ship-lap siding (any color), about 1" short of the full lengths of your replacment post, - - and 'rip-snip' them whatever width it takes so that the 'flange-edge' of the siding will accept the flange of your corner post, - - and the flat edge of your siding is wide enough to allow you to nail into your 'blank' corner (probably about 4" wide to the underside of your flange). In other words, - - you're effectively making an 'over-sized' sill trim out of siding. Keep about 1/4" from the top to allow for expansion, - - and that will leave you about 3/4" short at the bottom.
Once both sides are nailed in (accurately in place), - - nails every 16" or so is fine, - - take your new corner post and 'sqeeze' it into place.
Let the bottom of your corner flanges 'rest' into the bottom lip of your bottom pieces of siding, - - keeping in mind that corner posts usually sit 'lower' then the siding itself (match to rest of house).
You now have a floating corner post, - - that can't go anywhere.
P.S. A little trickier, - - but you could actually custom-make these 'over-sized' sill trims with aluminum coilstock, - - which would give the benefit of a thinner 'receiver-flange' profile.