I mean I am at the same office, requested they not send for Dec 14-Jan 1 on my Nov 18th test, and got Oath invite Jan 14th, for what that is worth
And I got DM day after test.
If you
don't tell them about your travel, they may also sent you an oath invite between mid and end Feb of course. Which would, I assume, be problematic for you
Special authorization is possible to get sure, but I imagine that's quite expensive and difficult and may interrupt your vacation especially if one has to wait in the city it's ordered from for a few days. I don't know anything about these but these things are rarely simple and I personally have a (Citizen) friend who ended up driving back to Canada from Rhode Island (ie: land border) because he couldn't get anything faster than 5 days from the Canadian embassy in the US to make a flight.
I believe you can use Indian passport for three months after doing Oath. But that said, CBSA may not be happy when you turn up with an Indian passport being a Canadian citizenship. And that is BEST case, worst case the airline realizes and refuses to let you board because the law is that you need a Canadian passport to enter Canada. Many people can't do this now due to the eTA, you not being from a visa exempt country and so not requiring an
electronic travel permit that they can check may work, but it's a risk in my opinion.
So to summarize, my suggestion is request they don't send oath invite until end of Feb.