I don't know the answer but I'd say you'd have to at least registered the accident with the HSA (can be done via their website) and informed your insurance company.
For a tax deduction to apply, an expense must be laid out wholly and exclusively for the purpose of the trade. There is a clear duality of purpose to medical expenses, with the main object being to restore the person to full health and the restoring of their capacity to carry on their trade being ancillary to that.
So the short answer is no, it's not a trading expense.