This is their itinerary (NOT RECOMMENDED):
Day 1 Drive from Kathmandu via Besisahar to Koto 2,600m; approx. 8 hours
Day 2 Trek to Meta 3,560m; approx. 7 hours
Day 3 Trek to Phu 4,080m; approx. 7 hours
Day 4 Acclimatisation day in Phu; side trip to Himlung Base Camp (4,800m)
Day 5 Trek to Nar Phedi, overnight stay in monastery 3,490m; approx. 6 hours
Day 6 Trek to Nar Village 4,110m; approx. 3 hours
Day 7 Trek via Kang La Pass (5,240m) to Ngawal 3,650m; approx. 8 hours
Day 8 Trek to Pisang (3,200m; approx. 3 hours) and drive to Besisahar approx. 4 hours
Day 9 Return to Kathmandu approx. 5 hours
My answer: NO, not safe (in terms of altitude)
We trekked Nar Phu in 2014 (Besisahar to Koto to Phu to Ngawal to Jomsom).
Driving to Koto (same alt approx as Chame) on Day 1 then trekking to Meta (3610m) next day is (i) too much altitude gain and (ii) for many, us included, too long of a day. Going to 4070m (Phu) on the 3rd day is too high too fast. It would also be a long day from Meta. Going from Nar over the Kang La to Ngawal in one day would be a long hard day.
The driving times seem very optimistic. It also optimistic to assume there will be space in monastery at "Nar phedi" (we did indeed stay at monastery, but room were limited). I think it took us 8 hours to trek from Phu to Nar Phedi (it was a longish day).
Trail from "Kang La Phedi" up to Kang La is fairly steep; Trail down from Kang La to half-way to Ngwal is very steep.
Nar Phu doesn't have a lot of tea houses. In 2014, they were in: Meta, Phu (very basic), Monastery at Nar Phedi, Nar. There were no "lunch stops" -- we had to stop and cook our own food.
Unless already well acclimatized (e.g., from recent preceding high-altitude trek) and in very good shape, one really needs camping for 3 nights.
Nar-Phu was a great trek -- why rush it?