British Carronades, brass guns, iron guns and howitzers could fire Shrapnell. It was a very effective round if the fuse was properlly cut. Shrapnell of the Napoleonic period suffered from premature ignition due to the friction of the balls. This was cured by Boxer in the 1840s and then the fuse problems in 1852. Interestingly 24-pdr Long Guns could fire 5.5in shells. The larger the Shrapnell Shell the more effective. The 6-pdr Shrapnell was not very effective.
Spherical case was introduced to the RA by Shrapnell although the idea and practice is older. He supposedly thought of this during the siege of Gibraltar when shells were fire from long guns. The Russians with their secret unicorns of the 1750s had a form of this with a bursting charge. It does not seem to have been used by the M1805 Unicorns. Interestingly there was a round for Russian siege mortars with had a bursting charge and musket balls.
The M1768 Saxon Granatstuck fired a spherical case round. The design showed lineage to the pre-7YW designs of the Prussians and the Russian Unicorns. It had a very interesting elevating system.
Shrapnel like shell from howitzers was effective against stationary targets where the range was known but was difficult against a moving target to get the length of the fuse correct.
The French fire shell from Naval guns and this is supposedly a reason for the destruction of their flagship at Trafalgar. The French tested captured Shrapnell in about 1812-13. My colleague Paul will correct me on the date. It was not adopted by the French.
Interestingly, the description of what Shrapnell was still misunderstood into the 1830s.