A qualified "yes".
First off, I am assuming that I know what you mean when you say "Constitutional Rights", being as there are no such things. There are 'natural' rights acknowledged by the uS Constitution in the sense that the federal government is prohibited from infringing on them. One of those is the right to defense of self and others. That right is as basic as they come. And in most cases, a lawful felony conviction does not in any way preclude the exercise of that right.
That said, if a person is deemed such a danger to himself or others that he is not considered to be stable enough to possess a 'weapon', then he should be isolated from society, period.
Keep in mind that many commonplace items can be used as weapons. Guns reach out further than most, and that is the sole rational reason that they are considered different from claw hammers. But combustibles and improvised explosives are far more dangerous and less discriminating weapons, and you'll never (rarely?) find an arrest for "felon in possession of gasoline".
I know this isn't particularly helpful to you in your situation, but I thought you deserved a more or less direct answer to your underlying question. And for me, I believe that someone who has transgressed against a vaslid law who has paid a suitable price for his transgression should be fully restored into society -- barring instabilities as described above.
