Here you go, looking up the Larig Ghru, Cairn Toul and Braeiach on the sky line. Corrour Bothy on the left.
As you can see no ice axe needed, their is snow forecasted for this weekend but it won't last long now as the ground is too warm.
When you say you want to start in Braemar, do you mean in the village or at the Linn of Dee car park? They're about 10km apart and there's no off road path between them, so a long road walk or short taxi ride to start. From the car park it's about 5km of estate road to Derry lodge and Bob Scott's Bothy. Corrour Bothy is about 8km from Derry lodge, the path is very well graded and dry apart from a short boggy section just after Derry lodge. From Corrour to the top of the pass just beyond the Pools of Dee is about another 6km. There's a short section of weaving around some large boulders just after the pass but not enough to require using your hands. After that you'll see a junction in the path, right for the Chalamain gap which leads to the ski centre car park.
The main path continues down besides the Allt Druidh through the upper Rothiemurchus forrest, this is a lovely section of the walk. At the bottom you come to a T - junction, turn right for Loch Morlich and Glenmore village - the T - Junction is about 7km from the summit of the Lairig Ghru pass. Loch Morlich is about 4km from the junction the village is 3km further.
If your going to Aviemore don't go to the village, turn left at the Loch. You can use the "Old Logging Way" this is a footpath/cycle path that parallel's the road. About 8km to Aviemore. There's no easy way back to Braemar, if there's a few of you it might be easier to split the cost of a taxi.
If you want to walk the Lairig An Laoigh back to Derry lodge. There's a YHA in Glenmore, Glenmore lodge also let out their rooms for the night. Or there's Ryvoan Bothy about 4km along the path from Glenmore village. Follow the signs to Glenmore lodge, go past the lodge past An Lochan Uaine (the green lochan) the bothy is about another km. You'll past the start of the Lairig An Laoigh path before the bothy, there's a big sign.
From the Ryvoan Bothy to the Fords of Avon is about 10km, there's a footbridge over the river Nethy but not over the river Avon (Arn). There's a "Refuge" at the fords, more a small shed than a bothy, usually full of German students, but there's loads of camping. Unless the river is high you should get across dry footed. It's around 10km from the fords back to Derry lodge.
If you want to walk back via Glen Feshie. At the T - junction at the bottom of the Lairig Ghru path turn left, go over the Cairngorm club footbridge and follow the footpath to Loch an Eilean. Take the path along the south side of the loch. There's a small bothy in the woods at NH 884056, just a wooden hut. The forest tracks will take you to Feshiebridge village 5km from the bothy. From Feshiebridge to Achlean farm is 8km of road walking, you're unlikely to meet many cars on that road so not much chance of a lift. Ruigh Aiteachain Bothy is 6km from Achlean the path is good apart from crossing the Allt Choire Chaoil stream which requires a scramble down one bank cross over the steeping stones and up the other side. Apart from that you could drive a landrover all the way. The bothy is brand new and very posh, even an outside loo.
Three km past the bothy the track goes through two ford where it crosses and then re-crosses the River Feshie there is a by-pass path on the left, it starts about 400m before the first ford. It's partly obscured by a fallen tree and not obvious from this side. From the bothy to White Bridge - on the Dee is 20km. The Linn of Dee car park is a further 5km.