The following is based on unverified behind the scenes information and has not been confirmed by canon sources.
The Silver Shroud bears a strong resemblance to 1930s pulp hero "The Shadow." Both characters are stealthy vigilantes with a mysterious demeanor, along with similar costumes, gleaming weaponry (The Shadow's M1911 pistols were named "Silver Heat" in the 1994 film reboot of the character), and catch phrases. The Shadow also has an analogue to Shroud's Mistress of Mystery in the form of his confidante, Margo Lane.
The Silver Shroud appears to be based on The Shadow and The Green Hornet. Like the Silver Shroud, they both had popular radio serials and wore a trench coat and fedora.
The design of the Silver Shroud could very well be based on "Silhouette" from the "Watchmen" comic series made by "DC Comics". Both characters are seen wearing a white scarf and the traditional jet black trenchcoat. In addition, Silhouette wears a complementary hat to their outfit as well as the Silver Shroud does. Silhouette
The Silver Shroud, both in name and appearance, also strongly resembles The Gray Ghost from Batman The Animated Series, in which Adam West played a black and white TV and Movie star that was young Bruce Wayne's childhood hero. The Gray Ghost character itself was an acknowledged tribute to 'The Shadow'.
Silver Shroud's Thompson sub-machine gun may be a tribute to World War II hero Mark Tennant, who was nicknamed the 'Green Hornet' by his fellow soldiers based on the radio serial character.
Emails on the terminals in Hubris Comics mentions that the producer wants to give Silver Shroud an 'English Butler'. This is similar to Alfred Pennyworth in the Batman series. Lamont Cranston, The Shadow's alter ego, also employs an English butler.
When Silver Shroud and Mistress of Mystery are spying on the robot-mobster meeting through the skylight, it is revealed that the creator of these robot-mobsters calls himself The Mechanist, similar to the Fallout 3 and Automatron DLC character, the Mechanist.
End of information based on unverified behind the scenes information.