Of course, deciding on an 'ideal' route that see's the least snow can only be done when you have up to date weather forecasts available within 2 or 3 days of your departure. This is not a major problem as you have no real need to book lodgings in advance and have the option to just 'wing it' or book a day or 2 in advance as you go.
Now if the weather played nice and you wanted to visit family in Vegas you could take CA89 near Mt Shasta to CA44/36 /US395 to Reno and then continue south on 395 past Mono Lake to Lone Pine and then take 190 across the wonderful landscape of Death Valley to Vegas. To save time and miles to Vegas you could head east to Fallon from Reno and take US95 to Vegas, but with "no less than 7 days available", 395 and Death valley is a lovely route and worth consideration. You would then head south on 95 past Hoover Dam and pick up I40 and/or parts of route 66.