if you pull the hose off again, you might (if it goes straight through the wall) be able to hold it up and peer out, you may be able to see the grille or flaps and a bit of daylight.
With the hose still off, turn the fan on and see if air is blowing out through the spigot. If it is blowing out of the spigot and the hose is clear, it should work OK.
Many hoods have a rear-facing spigot and an upwards facing spigot, the rear-facing one is used when the duct through the wall is directly behind the hood.
If the hose is a reasonable fit on the spigot, you can wrap duct tape or something to form a good seal and keep it in place. You will have to degrease well first. I find once the surfaces are extremely greasy and dirty, you need to scrub with Flash or similar, wiping will not do.
If the hose is not a good fit, you can get an adaptor. The hose and spigot are usually 100mm or 105mm diameter (about 4 inches). The flexible hose should preferably fit to, or push inside, a rigid round plastic duct through the wall.