At the risk of "teachjing grandma how to suck eggs":
Assuming you have a larger genoa
on a furler
on your forestay and a small jib
/ staysail that can hank on to your (detachable) inner forestay
In general, any furling
sail becomes progressively more poorly shaped as it is furled. General consensus is that you can only furl in about 20-25% of a furling
sail before it becomes functionally useless if you are trying to point (of course it may still be ok for reaching and running). Also, even though you can furl the genoa in further that 25% and still reach or run, the sail is probably made of a lighter cloth than the jib and exposing it to very high winds will likely strewtch it and shorten its useful life, whereas the jib / staysail will be made of a heavier cloth and better withstand high winds.
One other point: in very strong winds you will tend to reef the main, which moves the centre of effort of the mainsail
forward. If you also furl in headsail, this moves the centre of effort of the headsail forward, making for an unbalanced sailplan (possibly with lee helm). If you fly a staysail instead of a partly furled headsail (and furl the headsail in completely), you move the centre of effort back to balance the reefed main, for a much more balanced sailplan and probably less helm
So, carry your genoa in light winds.
In moderate winds either furl in a bit of your headsail or furl it all in and use the staysail (do the latter particularly if you want to be able to point to windward)
In heavy winds furl the headsail in and just use the headsail