Sweet potatoes stored in direct sunlight
Sweet potatoes are not in the potato family (Solanaceae) and as you say, do not develop solanine, or other glycoalkaloids such as chaconine. The only toxin they are listed as having in Medical toxicology of natural substances is ipomearone, typically produced in response to fungal infection. I cannot find any indication that is produced in response to sunlight. The toxicology book above says 'consumption of sweet potatoes has not been linked to human toxicity'. 

While it's hard to be completely certain, it seems to me that there are no reasons other than the likely higher temperature to avoid storing sweet potatoes in sunlight.