Statistically June is the month with the fewest gales in this part of the world. Also has the longest days and at this latitude it only goes to dusk at night not darkness.
Inverness to Orkneys is straight forward and the option of going into Scrabster is there if needed. Scrabster is big safe harbour that can be entered in bad weather
. The tides through the Pentland Firth are amazing, the North Sea drops something like 3 meters into the North Atlantic.
If the weather
is against you, then sailing in the Orkneys offers good sheltered waters rather than going around the outside.
Locals friendly and take the local fire water
Should be an great trip.