I have been in that area in the past 3 July's I started from Kvikkjokk on July 1 in 2010, it was a beautiful, very warm and sunny day, the next day it was cold, snowing and I spent a couple of days in similar conditions, after which the weather cleared. Higher up there will be snow and I have experienced some minor snow falls in each year, it can be windy and and with windchill quite cool. Also early in the season the rivers can be flowing quickly and deeper than normal, it is not uncommon for a bridge or 2 to be damaged by high water. However, in general I feel you will have no problem, yes mosquitos may be bad, but that depends a lot on your tolerance level. I will probably be up that way again next summer, but have no plan for where at this stage.
Enjoy your trip
A forum, still in its infancy, that maybe useful is the Nordic Outdoor Forum many of the members are experienced lapland hikers.
Reports of my trips can be found at Nordkalotteleden, Kalottireitti, Nordkalottruta