What is your state?
Your state of residence will determine this.
Someone said Michigan but not the OP.
While I don't recall all of Michigan's laws entirely offhand I do recall it is a state with a lot of restrictions. Including one of the only states that considers airguns under a certain size to be handguns and as such restricted items.
So pellet pistols perfectly legal elsewhere for anyone and unrestricted must be purchased as handguns in Michigan complete with obtaining a permit and having it registered. Something someone under 18 should be unable to do.
I also recall it considers long guns under I think it was 30 inches handguns as well, requiring a handgun permit and registration as if it was a handgun.
As such I would be quite sure black powder handguns intended to be fired and carried with powder and ammunition would be thus considered a handgun no different than a centerfire or modern handgun in Michigan.
As such minors are likely subject to the same restrictions they would be with any other handgun.
So the answer should be the same as it would be if it was any other handgun in Michigan and not specific to black powder handguns.
I see all kinds of restrictions against carrying handguns without a handgun permit, but don't know what exemptions for hunting there is.
However based on Michigans other laws I am going to presume a minor hunting with a handgun, which in Michigan should include any firearm, airgun, or anything else that expels projectiles similarly and is under a minimum size is less than ideal.
This may be confusing because federally they won't be considered handguns and may be obtainable in ways that other handguns are not, but will be considered handguns by the state of Michigan.
Some Clarifications...
The OP said they were a resident of Michigan
In Michigan an airgun with a rifled barrel is a firearm, and so an Airgun Pistol is required to be registered as a handgun, Michigan does not have a long gun registration so airgun rifles do not require registration.
The Michigan anomaly often referred to as a "Michigan Pistol" where a long gun 26"-30" long was considered a pistol in Michigan was changed to mimic the Federal length of less than OAL of 26" on Jan 1st, 2013. Interestingly, A "Michigan Pistol" 26"-30" long that was registered by the owner as a handgun prior to Jan 1st, 2013 is still considered a handgun in Michigan and can be carried concealed by a CCW holder.
Prior to 2004, there were interpretations of Michigan law that held Antique and/ or BP handguns were firearms and as such required registration etc. just like modern handguns. In 2004 House Bill 5427 was signed into law to Clarify antique firearm regulations in Michigan and became Public Act 99 of 2004, AKA "Janet Kukuk act". Today in Michigan, a BP revolver is considered an Antique and/or replica and not a pistol or handgun so there is no specific age restriction on their possession.
Michigan does not have a minimum caliber requirement for hunting with muzzleloading rifles, muzzleloading shotguns, or black powder handguns, but they must be loaded with Black Powder or a Black Powder Substitute. They can not be loaded with smokeless powder.
There is no specific restriction prohibiting a 17 yr old from possessing or hunting deer with a black powder revolver, and a 17 yr old does not require adult supervision while hunting in Michigan.