Seems to me that you took off with a valid observation and forecast, and lacking other information, you could use the last valid observation you had to satisfy the legal requirement for landing weather. Every airline is different. Our FOM prohibits a visual approach if it is the captains first time at a particular airfield.

Someone else alluded to captains authority, and I agree. If, in the captains judgement, it was safer to land than to divert, then that's all he (or she) has to say to anyone who asks. End of discussion. That's why we get paid the big bucks! Safe, legal, reliable. In that order.