The avalanche risk is usually higher the later you go in spring. That being said, there are many, many perfectly safe places to sled here when the risk is high. Renshaw and Belle (Lucille seems to fall apart first) all have great spring sledding. Use your common sense and your avalanche training to stay away from trouble spots.
If you are not sure, talk to one of the locals that have their avalanche training certificates. They know the areas very well and can steer you away from the bad spots. The trained locals that I know of and trust are also with Search and Rescue and are experts on sledding McBride. Rod and Steve from Adrenaline Tours are your best bet to talk to (or to hire as guides which is even better). "bbtoys", if he is around, is always happy talk to fellow sledders, has his avalanche and SAR training and is extremely knowledgeable.