Well the shoot every thing you have no matter what bunch is on board, but I would urge some caution. Two things come to mind very quickly.
The combination of caliber (.44-40), finish (nickel plate), and 7 1/2" barrel was not commonly made, and its value should not be determined by current values of past cataloged options. The total number in existence (not counting commemoratives) is probably in the low hundreds and maybe substantially less.
While it is very decorative, nickel finish can peel and flake if you shoot it, especially around the cylinder's front face. Even the Colt company advises that this particular model is made primarily for collectors, and they can be expected to sharply drop in value if they are fired. Of course those that are insisting that it must be shot have nothing to lose.
In addition, at the present moment the Colt Company is in the middle of bankruptcy proceeding, with the final outlook completely unknown. What ultimately happens might have a substantial affect on your revolver - in an upward direction - if it remains unfired.
Also with it's relatively crude fixed sights, and chambered in a somewhat difficult to find cartridge, the revolver has little to recommend it for the purpose of deer hunting. If this is the primary use you would put it to, you would be better off to sell it to a serious collector, and use a part of the return to purchase a Ruger Super Blackhawk, chambered in .44 Magnum, with a 7 1/2" barrel, and easier-to-see/fully adjustable sights, with a blued finish.
Unlike the Colt, it is designed and made for the purpose you have in mind.
In any case before heading for a shooting range with the gun you have, I suggest you call and discuss this situation with someone at the Colt Company. I am sure you'll find what they say is far different then some of the advise you are getting here.