You might find something suitable here - V E , otherwise known as Vertical Explorers
Pakistan. I've taken K2 Gondogoro La and Snow lake trips with them and even though I've always been a confirmed solo traveller I enjoyed these trips so much that I don't hesitate to recommend them. They offer travel packages all over Pakistan for groups and individuals with good quality for reasonable prices.From my initial enquirys with them to booking and payment to finally using their services in Pakistan, everything went smoothly.
Have a look at this: Lost on a Glacier in Pakistan
There's a French company that does ski trips Biafo-Hispar via Snow Lake in April, so May might still have too much snow for walking easily, especially for the porters. Late June should be fine. Partly, it depends on the previous winter/spring. I've heard they had a pretty hard winter, with lots of snow, but haven't completely verified that.
It is shortcut for going to South of Xinjiang from the north or to the north from the south on Ancient Silk Road. It is just 6-day trekking,but on they way you may see various landform, wild animals,acient ruins. It is the top grade classical route in Xinjiang.
Now it had existed for hundreds of years, it was abondoned since the highway going through Tienshan Mountain near Urumqi was built in last 1950s.
There are some high mountains like Xuelian Feng, Tomur Peak,Pobeda,Khan Tengry peak,Koxkar peak are in this area.
Biafo Hisper is the best and callsical trekk,its required 3 week islamabad to islamabad,there is some other trekk but they need more days,exemple Kurdopin pass snow lake trekk,Braldu lukpe la snow lake trekk,and the most beautifull trekk is SIMLA pass snow lake trekk,this trekk is only the one from where you can see all 8000m peak which are situated in karakoram baltoro.
for more information pm me