There's no contraindication with your specific type of heart block for taking beta blockers, just guidance to prescribe with care. So ideally a more targeted blockers like Metoprolol rather than Propranolol for example. And at the lowest possible dose to give effective relief.

Heart block when sleeping is a fairly common finding and not too concerning. Obviously I don't have your medical records or anything and nothing I am saying here constitutes medical advice, but if a doctor had looked at things like holter recordings and told you that it's fine, then I would be inclined to believe them. As long as your HR doesn't drop too low during sleep naturally, beta blockers should be fine.