OOB wise these ominous "Chasseurs Corse" are only in the 1805.oob and Augsburg.oob. And there they are in the same place that the Carab. Corse usually takes, 5th Division of Seras Brigade of Gilly. I can only suggest to replace the "Chasseurs Corse" in these OOBs simply with the "Carab. Corse" unit, "Chasseurs Corse" is obviously a different/wrong depiction of the "Carab. Corse".
Uniform wise the "Carab. Corse" seem to have carried a uniform roughly similar to that of the French light. the above linked page describes:
"A new uniform is intended for him to replace his outfit in brown-brown cloth. This one is described as follows: Habit jacket of dark celestial blue cloth, panties of the same, vest of white cloth. The lapels and the facings of the coat are daffodil, the collar dark celestial blue. white metal buttons with the inscription Corsican Legion. For hair shako.It seems that this outfit was first distributed only to the elite battalion formed with the help of each of the rifle companies formed in September."What ever it is, it is surely not the Chasseur uniform that it currently has in the OOBs. The following OOBs need to get the uniform number corrected to 8 instead of 19:
Caldiero_Campaign.oob
Italian_Campaign.oob
Moravia.oob
Moravia_Alt.oob
And for the "Tir. du Corse" you want to correct some OOBs to make sure it has NOT the usual brown uniform.
The following OOBs use the French legere uniform(number

instead of the brown uniform(number 164):
Austerlitz_cav-regt.oob
Austerliz.oob
Danube_Campaign.oob
Italian_Campaign.oob
Ulm_Campaign.oob
All other OOBs use the brown uniform.
I hope this completes you confusion.

To sum it up:
1. Replace all "Chasseurs Corse" with the single "Carab. Corse" unit.
2. Give all "Carab. Corse" a French legere uniform(number

.
3. Give all the "Tir. du Corse" the correct uniform(a modified French legere uniform based on number 8 or 9).