Does simmering sparkling water change/decrease its mineral composition significantly?
No, simmering sparkling water should have negligible effect on its mineral composition.

You're exactly right that simmering it will drive off the $\ce{CO2}$. This $\ce{CO2}$ leaves as only/exactly $\ce{CO2}$ molecules, and any minerals that might have been associated with the carbonate/bicarbonate $(\ce{CO3^{2-}}/\ce{HCO3^-})$ will remain behind in the water.  Most such minerals will be present in dilute enough of concentrations that they will remain dissolved in the no-longer-sparkling water, as long as only a relatively small amount of the water itself is boiled away.