I have only seen one type of hand vase, in fact it is more likely a toothpick holder, made in pressed glass, that remotely looks like the S. of L.
I do not have one in my collection but it is pictured in the book "Victorian Glass Novelties" by Jo & Bob Sandford. It actually looks like a hand holding a flaming torch.
Hand objects were very popular in Victorian times, & many variations on the theme were made. In porcelain, there were hands holding seashells, sheaves of wheat, pineapples, (a Minton design) fans, & so forth.
Worcester made a well-known hand vase known as "Mrs. Hadley's hand" designed by James Hadley, supposedly modelled after his wife's hand.
There were many brooches featuring hands holding bouquets or fans, & rings made in the form of clasped hands.
Brass letter clips were made in the form of a lady's hand, also.
In glass, the trumpet or cornucopia shape vase tends to be the predominate design, but there are also hands holding bottles, fans,(used for pin dishes & toothpick holders), cups, & sheaves of wheat.
There are also glass bottles or decanters shaped like hands holding guns & daggers. These are either marked either "Depose" or "Geschutzt"- patented.
I believe that there may have been some items directly inspired by the S. of L. but the design is too widespread for all hand items to be directly related to it. The hand, nearly always an elegantly lady-like one, featuring a lacy cuff, was a typical Victorian motif, a throwback to Classical symbolism updated to suit the fashions of the day. It has sentimental allusions, which fit in perfectly with the Victorian sensiblity.
I have even seen a Victorian wax severed hand under a dome, accompanying a typical display of wax fruit & flowers!
Following is a photo of part of my collection of hand vases. There are vases from the Victorian era to recent (1990s) ones by Fenton.