While doing the Portuguese central route, I've swam in:
- the Cávado river (there's a beach to your right as you cross the river from Barcelinhos to Barcelos. Water gets deep very quickly, pay attention.
- Neiva river, about half-way between the Albergue in Tamel and Vitorino dos Piães. You cross over via an old roman bridge, there is a tiny sandy area to your right. Always very cold water, nice tiny spot for a rest.
- Minho river, there is a tiny sandy spot by the river as you get near the center of Tui, but also some quiet grassy spots just before.
- Verdugo river, large-ish beach in Pontesampaio, on the other side from Arcade. Close to the ocean so you may notice saltier water.
In July and August these will have good temperature, but for June the temperatures will be at low to mid 20s at best, so not sure it will be very appealing.
Personally, I'd say, check the forecast for your expected travel days, if its sunny a dip in the water always feels nice and the shorts weigh next to nothing. Alternatively take synthetic walking shorts as well as trousers, you can always use those.
If you are going on the Coastal route, better take a neoprene suit to swim in June
or a brave heart...