The bigger problem is the colour shift that occurs - especially in blue skies
As well as monitor profiling, there are two other potential sources of discrepancy:
1. The profile itself is never 100% accurate. Even if it were 100% accurate on the printer that was used to create the profile, the unit you own probably produces slightly different colour for the same RGB value.
2. Monitors have a greater range of saturations than printers do, so they can display colours that cannot be printed. Set your soft preview to the profile you are using to print, then turn on Gamut Warning. Any colours that are displayable on a monitor but not on the printer will be greyed out.
If you have profiled your monitor and if you have followed Ian Lyon's instructions and if the blue is not greyed out by Gamut Warning, then what to do? Create a Curves layer that compensates for the problem, and save that layer for use with all other print jobs done with that profile and paper. For example, if the blue sky has a greenish cast, then create a curve with reduced green in the upper portion of the curve (skies are bright). Write off-line if you need help with this.