The total tax paid is generally the same whether salary or dividend route, the difference is whether the employee or employer pays it
Indeed, and in most scenarios where the business proprietor pays himself using divis, it is totally the case of the business being no more than a vehicle for his livelihood which he is free to run as he wishes (let's face it, what else is the purpose of a business?) so dividends do no more than avoid NIC.
I am not a tax specialist but I don't think there is any income tax saving, in any scenario.
Most instructors I have known were SE and some got as little as £10/day retainer. But they were all thumbing through airline job ads the whole time anyway and if I was the employer I would obviously strongly disapprove of that, especially so openly before customers. The tolerable attitude is different between a PAYE person and a SE person.