Just putting the stick in your vice will achieve nothing - you need to apply the "reverse bend" principle. This means that you put exactly the same bend to the stick but in reverse to where it currently is; the only thing you need to think about, though, is whether you can wait for some time for the wood to season. For a piece of Hazel of a suitable size for a stick this is likely to be about a year, ideally. You need to leave it somewhere dry but with a good airflow, and lay it on it's side, not stood on end and/or leaning against a wall or some such.
If you take a piece of 25mm ply or similar, lay the stick lengthways on it, then mark the shape of the stick; cut along the shape you've drawn, seperate the two pieces from each other on a flat bench, then lay the stick into the gap but the opposite way round to the way you marked the cut, then clamp the two tightly together forcing the stick to take on an exact "reverse bend" to that which it had. You can then leave it like that for as long as it takes for the stick to re-shape. I've had very good results from this method for many years, the great advantage of it being that there's no requirement for steaming.
I used to make high-end carriage driving whips and the Holly and Blackthorn used for these needs to be very straight and these woods also take a lot longer than Hazel to season. One method I used successfully with these was to hang them from a beam, thin end uppermost, and then attach a weight to hang from the bottom end for the entire length of the seasoning. This needs to be a substantial weight, circa 15 kilos, I used full and part-full propane bottles for this; it's a great way to ensure perfect stability in the shape of the stick as it pulls all the lignin in the wood into line, but it is a waiting game...............
If you google "steam bending sticks" you'll get a host of useful stuff to read, but it's not always neccessary to use the steaming method - sometimes you can straighte a very mis-shapen stick in minutes by bending across
your knee with the reverse bend...........................I hope some of this helps.................................