Overhaul is different to modifying a ship.
This overhaul as, a full service maintenance, changing spark plugs, gears and cogs.
Now changing a ship design by "Refit" does mean a overhaul needs to take place first, after that is complete it will then refit the ship.
You should be able to refit any ship but, you will pay a build penalty based on how different the ship is, in regards to components.
You want to overhaul a ship, after a number of years because the condition of the ship actually causes more breakdowns, I generally as a rule of thumb aim between 5 and 7 years for an overhauls, but you decided what is best for you , as overhaul tend to take offline your military ships for a period of time while the maintenance is being complete.
To modify a ship, you copy your design and then make the changes, once this is complete you change your shipyard to produce that design and the 3rd step in the build shipyard menu is to refit the ship to that new design.