Thankfully this is not the case. The 550/50 requirement is for if you're using it to put down animals when legal, CPW confirmed there are no requirements other than general Colorado legality for what defensive arm you can carry where hunting.

I visited with Bob Thompson, our Assistant Chief of Law Enforcement, about the question. Bob’s guidance is pretty clear on the proper use of the handgun in the field. The paragraphs below summarize the issue. Bottom line is the first sentence. There is no “backup handgun” for hunting big game, the manner of take allowed is what is prescribed for the season and the license.

There is no such thing as a back-up sidearm during hunting season. You may carry a handgun with you during the act of hunting for personal protection but that is the purpose. There is no specific requirement for a legal handgun for personal protection (barrel length or caliber)except that it is in legal possession of the person under Colorado Law.

The use of a handgun to “put an animal down” would only fall into use during a rifle season and then the handgun must be in accordance with a legal method of take and meet the criteria listed in the Big Game Brochure, i.e. At a minimum, it must have a four-inch barrel, fire an expanding bullet of .24 caliber (6 mm) or larger and use a load that produces a minimum 550 ft. pounds of energy at 50 yards. Shoulder stocks or other attachments are prohibited.

Colorado Parks & Wildlife -
Lesson 3