I know that hydrogen halides can react with each other to produce halogen halides.
As an example here is a reaction between $\ce{HCl}$ and $\ce{HF}$: $$\ce{HCl + HF -> H2 + ClF}$$
As for the mechanism it is like this (taking into account that chlorine is hypervalent but fluorine isn't): $$\ce{HCl + FH -> HCl\bond{...}F + H. -> H. + ClF + H. -> H2 + ClF}$$
I know that both of these are acids and that $\ce{HF}$ is weaker than $\ce{HCl}$. However with the halogen bond the negative charge on the fluorine (partial negative after the formation of the halogen bond) is more delocalized. This stabilizes the $\ce{H-Cl\bond{...}F}$ intermediate and makes the dissociation easier for the hydrogen and harder for the fluorine. And yes the hydrogen radical is very reactive but that is exactly why $\ce{H2}$ forms in this process.
But I could see some problems with this.
It would have to be in a vacuum for it to not be explosive(most reactions involving fluorine or fluorine compounds are explosive because of fluorine's high electronegativity (same reason reactions with $\ce{O2}$ burn things))
If it is in air $\ce{O2}$ could react very violently with both the chlorine and the fluorine giving you these products: $\ce{ClO}$, $\ce{ClO2}$, $\ce{ClO3}$, $\ce{ClO4}$, $\ce{Cl2O}$, $\ce{Cl2O2}$, $\ce{Cl2O3}$, $\ce{Cl2O4}$, $\ce{ClO6}$, $\ce{ClO7}$, $\ce{OF2}$, $\ce{O2F2}$, $\ce{ClO2F}$, $\ce{ClO3F}$
Chlorofluorocarbons could also form from reactions with carbon based compounds in the air like methane and $\ce{CO2}$.
And this is all because the halogens are very reactive.
Similar things would be true for other halogen fluorides.
So is there a more practical way to form halogen halides than reacting $\ce{HX}$ with $\ce{HY}$ where both $\ce{X}$ and $\ce{Y}$ are halogens?