I was wondering, whether there is some summer variant of biathlon - without cross-country skies. It might be fun to try racing on inline skates with shooting sessions. Is there already anything like that?
Yes, in Germany you can take part in a summer version organized by the DSB (German Shooting Federation) that consists of running (in shoes) and shooting.
Although this is the main variant, according to the rules:
Summer Biathlon is an international competetive sport, combining two different sports. Competitions of the DSB (German Shooting Federation) mainly combine Cross country running with shooting with small-calibre rifle or air rifle. Other combinations are possible for competitions, but are not carried out as "German Championships". These could, in addition to cross-country and shooting, consist of rollerski and shooting (Roller Biathlon), Inline/Cross-skater (Skike) and shooting, mountain biking and shooting, whereby in addition to shooting with small-calibre rifle and air rifle, also laser rifles can be used, particularly in urban or introductory events.
(my translation, and my bold)
I assume these biathlons with skates are mostly locally organized, and the local shooting club (Schützenverein) would have details.
One link I found was of a team relay event in Saxony