You're going to be tracked because you're going to obviously be starting a colony without any kind of legal authority in the sovereign space of another nation. We're talking about the displacement of tens of thousands of people and an absurd quantity of apecialized equipment you're going to smuggle all at once on a secret fleet that is going to maintain operational secrecy at a level that gets the CIA harder than diamond, and that's assuming a suicidal population that's going to isolate itself completely in a somehow hitherto unknown garden world that's perfectly suited to human life. There's a reason why colonization is a state-driven process for the most part in sci-fi. You need factories, experts - it's an insane endeavour to hope to do this without any authority figuring out you're about to completely annex an incredibly valuable strategic asset within their border. And the whole reason humanity is settling the Traverse is that the Council isn't letting them settle the much more stable regions of space. This 99% number is a red herring.
They're settling in the Traverse because they still want to be part of galactic society - to make money, really - and thus are sticking to the Mass Relay network and vicinity. But that logic doesn't apply to anyone willing to go to Andromeda, because they're irrevocably cutting themselves off anyway.
The 99% number isn't a red herring, its a logical outcome of the slow speed of travel relative to size of the galaxy. There are vast swathes of the galaxy that are months if not years of travel away from anywhere that can meaningfully be considered Council space. That have never been visited and may well never be visited by a Council ship.
There's no lack of space in the galaxy, there's only a lack of space on the Mass Relay network. If you're willing to leave the network, the only reason to leave the galaxy really is the Reapers.
(Or if the Mass relay network had a connection to Andromeda, that would make sense. But the duration of the journey suggests otherwise)