Discoveryplus.co.uk £6.99 for 1 month or £29.99 for 1st year (then £59.99) or Eurosportplayer.com not sure of the price.

The women's 10m rifle was on Eurosport 1 but no other shooting that I could find.
I even set the sky box to 'record series' for Olympic shooting but it hasn't recorded anything else.

Oh, just found Eurosport player is moving on to Discovery+ so same price.