Shinkansen trains run via Shin-Fuji Station, not via Fuji Station.
And, you donft need to travel via Shizuoka Prefecture to get from Yamanakako to Narita International Airport [NRT].
- japan-guide.com: Lake Yamanakako: Access
http://www.japan-guide.com/e/e6908.html#jump_accessWhat time do you think I need to leave in order to get to the airport in time? Where around the lake is your accommodation? Do you know a bus stop located nearby?
I recommend you travel early to the airport for a case where the transportations happen to be delayed.
If you can catch the highway bus #1104 (for Shinjuku Expressway Bus terminal) scheduled to depart around 08:25 - 08:40 from bus stops along the lake, you can get to the station in your NRT terminal by 13:20.
I will be travelling to Okinawa on the 17th, and my flight is scheduled to depart at 14.50. Your flight is Vanilla Air #805 to Naha Airport, right? If so, your terminal is NRT Terminal 2 and you need to check in by 30 minutes before the departure time, i.e. by 14:20. (NRT-bound trains make a stop at the station in Terminal 2 just before arriving to Narita Airport Station in Terminal 2.)
If your Vanilla Air fare type is Inclusive, it is worth considering flying instead from Tokyo International Airport [HND, Haneda Airport] by JAL or ANA with a discount air ticket. (NRT is located actually outside Tokyo Metropolis and much further than HND from Yamanakako.)
- japan-guide.com: Discount Air Tickets
http://www.japan-guide.com/e/e2364.html(1) Highway bus #1104
(Regular cost: 2100 yen per adult from Yamanakako Hirano)
: Yamanakako Hirano {8:25} ---- Bugakusou-mae {8:28} ----
Yamanakako Asahigaoka {8:35} ---- Yamanakako yakuba-mae {8:37} ----
Yamanaka-kyoku-iriguchi {8:38} ---- Fujisan Yamanakako {8:40} ----
Kawaguchiko Station {9:10} --//-- {10:55} Shinjuku Expressway Bus terminal.
(2a) JR Ltd. Express Narita Express 23
(Regular cost: 3190 yen per adult with a seat reserved)
: Shinjuku : Track 5 {11:40} --[JR]-- {12:54} Airport Terminal 2.
(2b) JR non-express train and Keisei non-liner trains
(Regular cost: 1440 yen per adult with a seat reserved)
: Shinjuku: Track 15 {11:48} --[JR]--
{12:09} Nippori: the transfer gate: Nippori {12:18} --[Keisei: Limited Express]--
{12:31} (Keisei) Takasago (via the same platform) {12:32} --[Keisei: Access Express]--
{13:14} (Narita) Airport Terminal 2.