Seems like a customer appearing to be unreasonable (even if that wasn't the intention) along with a company that aren't dealing with things as fast as they arguably could, even if there's nothing illegal about that.
If I got the OP's email, I wouldn't be particularly enamoured of them and I would probably want to make clear that we weren't responsible for any indirect costs (eg bike hire) but at the same time would be trying to work out how to sort out something for the holiday (a test bike loan, for example).
Regarding the 'month', I don't think that's the right time to claim. They've said two weeks to inspect. I don't think you can reasoably include the time from notifying them to them actually getting the bike. While two weeks to inspect is a bit longer than I'd hope, at the same time it's not ridiculous or unreasoable as such I reckon and is just part of the downside of buying online which is offset by the price.
I guess that the question is how long after that two weeks it'll be before you get your replacement. Assuming that it's reasonably fast (a week, two max, I reckon) then I don't really take much issue with Canyon other than suggesting that maybe they get people who can phrase emails better.