According to the write up on the Cherry's Fine Guns website, it's named the Zimmer pistol:
4.5mm Caliber Percussion
Reproduction of Belgian pistol that features an walnut stock with traditional fluted grip, enriched with a typical metal buttcap. Provided with front and rear sights, it is produced with round barrel and color case hardened frame. Weight 1.1 lbs.
S335-4.5mm 4.5mm caliber percussion $430.00 (Special Order Only)
(add $20.00 shipping and handling)
Of similar interest is that Pedersoli also makes a 4.5 mm training barrel for their Napolean LePage target pistol which are produced in calibers .31, .36, .44 and .45 smooth bore:
And Pedersoli also made their fixed barrel Saloon target pistol in .36 and 4.5 mm, which has a box lock action and grip shape somewhat similar to the Zimmer but with a heavier round barrel.
Cabela's also seems to have discontinued selling their latest production of a parlor pistol which was a short barreled Derringer type that used 209 shotgun primers.
But they were also selling a parlor rifle percussion cap model for a while. I saw one on clearance at my local Cabela's which probably indicates that it has also been discontinued. I recall reading that some folks thought that it was underpowered and somewhat more difficult to load small pellets into the longer barrel.