The Cairngorms could be fine in the Glens and possibly even some of the Bealachs will be reasonably passable up to 750m if you don't mind a bit of pushing and/or there hasn't been too much snow.
The best routes in the Cairngorms involve river crossings and even if the rivers aren't high from snow melt, they are reasonably deep and fairly/very cold at this time of year. You need to seriously factor in regaining body heat after crossing, even if only up to knee level! If you find out which YHA and independent hostels are open and aim to arrive at these each night, then regaining body heat is not so big an issue. If you are bivvying I would imagine it becomes very difficult. Staying in a bothy, but with with no fuel for fire is doable but you need to choose your dry kit, sleeping bag and food carefully, especially if air temp in <5C.