As either Norway or Sweden England is very often a valid supporter. It is entirely possible to win it against Denmark and Norway/sweden etc. provided Denmark doesn't have a strong ally (they sometimes ally Muscovy). If you are going to declare and rely on help from England (sometimes you can get Scotland too, which is nice. Keep England and Scotland workign together for a while) it is helpful to time the war so that they are done with the War of the Roses / are not in a war with france at the time. If those are active, their troop contribution can be unreliable.
As has been mentioned, it's feasible to simply do it on your own (especially as Sweden) but it can get real costly and if you are not an experienced player (in which case I suppsoe you wouldn't need to ask the forums for advice on this) there's no guarantee it would work.
Things like being ahead of them on military tech helps and otherwise being patient and only fighting when the terrain is good for you will help. If you'r egetting supprot from other nations, let them fight the battles if possible to save you the trouble and the cash. I am a fan of making sure that when you win the independence war you take as much land as the warscore will allow. If Norway vs Sweden/Denmark I prefer taking most stuff from Denmark, but Dalaskogen from Sweden is almost a must and if Aggressive Expansion permits Sjælland from Denmark is vital too.
With regards to the comment of grabbing it pre/post 1450... If the setup is bad for you and you don't feel confident that you can win with your current supporters and things, you can absolutely wait, but the longer you wait the more power your neighbors can consolidate. Worst case scenario you wait, Muscovy swallows all of Novgorod and consolidates power in the east, Poland has Lithuania in a union and eats the Baltics, Austria stays emperor, England eats Scotland, Denamrk annexes Holstein and acquires another ally, and you gain no new supporters or even lose some. Waiting can also be a risk. As Norway you may get Sweden's help which will let you win the war, but it gets trickier to get the things you want from the war. As Sweden Norway will never aid you and your potential list of allies will typically remain thin.
Waiting for Denamrk to be in a losing war is a bad bet as it could take a hundred years for them to get in a war at all.
However. TL;DR: to become independent all you have to do is declare a war and win, doesn't matter how you do it.