it is not fun to do especially if the blind nails are close to butt edge . you are basically doing what we do on a new install but after the siding is installed.( we do not pie cut them and are held in place with blind nail)
we still caulk at all trim boards we use geocel due to the many color choices (will make it to the color of prefinished hardie) and how well it works but it is not an easy product to tool http://www.geocelusa.com/
"be careful at listening to just one persons advise" said me
"be careful at listening to just one persons advise" said myself
p.s. not all i say is a fact but not all i say is my opinion.
cut out old caulk and buy really good quality caulk to replace it( as flexible as possible) . you do not know that they flashed correctly behind the butt joints and caulking keeps the water out, it might need caulking again in five years but by then you might need a new paint job so it falls right in the time line...