Generally standard soldering wire rolls always integrates flux/resin to corrosion protection of the metal once the component was soldered on the boards.
Now, we can effectively found a lot of soldering products with more on less chemical protection against corrosion.
But in general, as you are soldering with standard solder wire, you will always have resin around and at end, the board doesn't looks really good and it's very difficult to detect any potential dry soldering point.
The very easy and cheapest way to clean the boards without any damage is to use solvent (same base as our wife's used to clean their vernish they used to paint their ongles/fingers). This kind solvent (acetone) will totally clean you boards and the result is very good.
Just use it with a brush to clean all the resin and soldering paste... Few seconds and that's ok...
Simple but efficient and very cheap ( around $3 the Liter).
I make a few thousand pcbs a year and rarely clean them with no issues yet with board failures due to corrosion from the flux. Depending on the end user the pcb is for I either leave the pcb as is, clean it with aerosol flux remover and then coat the board with pcb lacquer or else I clean the pcb with a toothbrush dipped in metho. The toothbrush dipped in metho (or isopropyl alcohol if available) works great. For pcbs that have no green solder resist on them the residue that is created by "cleaning" with alcohol leaves a protective coating on the boards. Unlike bare copper boards that have no treatment of any sort the alcohol cleaned boards look identical years later with no signs of oxidisation.
If the boards are going anywhere where there's going to be exposure to weather/humidity and the boards are bare copper then I'd recommend that they get some sort of treatment as a minimum.