Where are you looking to vent the fan? Most kitchen fans have axial blades designed for mounting in a wall / window and venting directly outside without any ductwork. If your chimney is on an outside wall, you could wall mount the fan inside the chimney and vent it outside, but if the chimney is open at the top then it will be less effective, as it will only pull a limited quantity of air from the kitchen, as some air will be pulled in from the open end of the chimney too.
The other problem is cleaning. Hoods have washable filters, release a couple of clips, pop them in the dishwasher and they're done. Fans have to be dismantled, cleaned and re assembled, and believe me, above a cooker they will need regular cleaning. I'm not sure how accessible that would that be. Could you stand on your cooker to clean it?
Cooker hoods also use centrifugal fans, these produce higher pressures that can be used with a run of ductwork connecting then to a remote outlet.
Having said that chimney fans that are used for fires with smokey chimneys can also be used for ventilation purposes. They are installed on the top of the chimney outside. For an example
click here My only concern here is that the whole of the inside of your chimney may become greasy overtime.
I would fit a hood and then if its in built lights weren't satisfactory find new lights to go with that, rather than the other way around.
