I'll gladly answer, as I have trekked Sarek before in 2010, and also have months of experience on Kungsleden/Nordkalottleden/Padjelantaleden and various other trails in the region.
On helicopter flights
I cannot personally condone helicopter flights for anything where they are not absolutely needed. They are loud and ecologically wasteful and they seem to be a nuisance for most trekkers and also many of the professional staff at the occupied huts / Fjällstations that I have talked to. I realise that some flights are required due to logistics and SAR, but I honestly think that the late increase in personal convencience or recreational flights is awful and to the detriment of the environment and the enjoyment of the outdoors by many people in the Fjäll.
So having said this, I would love to encourage you to think about other ways for travel to and from The Great Outdoors: Swedens public transport network is fantastic, and you can easily reach many entry and exit points to Sarek via train and bus connections.
On the route
10 days is probably on the shorter end for a full Sarek crossing, at least if you want to go right through the middle. Note that it is certainly doable, but I would suggest against it because:
- Sarek doesn't have established trails. You will find some tails to follow, but sometimes you will have to trek off-trail, making progress a lot slower.
- Essentially every single river and stream has to be forded, this will cost considerable time.
- I would suggest planning at least 2-3 reserve days in case you need to change your route. This can happen due to weather (e.g. swelling rivers, making fording impossible), injury/sickness, navigational mistakes or other reasons.
- You'll have to carry a fairly heavy load for a crossing, due to needed gear and food supplies. This puts a further limit on your speed. IMHO Sarek is not the place for ultralight camping.1
Note: feel free to ignore some or all of my advice - if you are considering a Sarek crossing I assume that you are an experienced outdoorsman, and your mileage and your willingness to take risks might well vary.
From the North
Bus from Gällivare to Ritsem, there is a boat to Akkastugorna, where you can follow the first kilometers of Pajelantaleden to access Sarek from the north
Bus from Gällivare to Ritsem, but exit at Suorva (probably have to ask the Bus driver for it) or Vietas. At Suorva you can cross the Suorvajaure on the artificial dam, at Vietas there is a boat. Once across the lake you can walk into Sarek from the North-East.
From the East
Bus from Gällivare to Ritsem, get out at Kebnats and take the boat over to Saltoluokta Fjällstation. There you'll find the Kungsleden and access to Sarek from the East. You can also continue Kunsleden to the south until you reach Akse, and then turn West into Sarek.
From the South
Bus from Murjek/Jokkmokk to Kvikkjokk, where you can follow the Kungsleden to the north, you can split of at many points towards Sarek (e.g. Partestugan, Partekietle) lying to the West of Kungsleden.
Both Gällivare and Murjek are reachable by train.
What I have personally done:
We took the route in via Ritsem and the boat to Akkastugorna. We then travelled far into Sarek over several days, until a thunderstorm let the rivers swell to sizes where crossing the bigger ones would have been purely suicidal. Eventually we took a roundabout way back towards the north and an exited through the same boat we came near Ritsem. (We decided for this this mainly because we knew that there were further big river crossings planned for later in our route, and we did not want to get stranded 8+ days into a 12 day route, with un-fordable rivers between us and the extraction point.)
1 Scandinavian weather can be rough as hell, even in mid summer, and consequences of anything happening in Sarek are real, with help being days or weeks away.