Just wanted to clarify you didn't make a typo here:
"They also asked what would I do, if the crosswind was, let's say 34 knots and the max allowed for take off was 35 knots."
My immediate thought would be if I'm a professional pilot being paid to (a luxury today!

) work for a business I should be expected to willingly operate the aircraft within its safe operating limits. 34knts is within these limits if max allowed is 35knts!
Am I missing something here or did you get the figures wrong? Just wondering, not a criticism - I've only got circa 10hrs in about 10 years!