You could try a dealer, but they'd pay wholesale prices. 1906 is a fairly common date for Liberty Head nickels so unless it's in better than average condition you're not likely to get more than $10 to $15 for it.
Alternately you could find a local collector who'd be willing to pay a price close to retail, but you'd also need to know the coin's condition more accurately before selling it privately.
1906 is a common date for Liberty Head nickels, most circulated coins are valued at $1.00-$3.00
The only silver nickels ever made were made in 1942-1945. These nickels contain 35% silver. So a 1906 US silver nickel is worth nothing because there is nothing like that. See the related question below for the value of a 1906 US nickel.
The value of the 1906 V nickel varies greatly depending on the condition of the coin. This nickel can be worth as much as about 4 dollars depending on its definition.
There is no such thing as a 1906 Indian head nickel(*). The first nickel with that design was issued in 1913. The previous design is called a Liberty nickel; you can find a list of prices at the attached link.
It's not silver, but it should be worth from about a dollar in Good condition and up to $70 if uncirculated.
It's a Liberty Head Nickel the date 1906 is very common, values are at $2.00-$5.00 for average coins
A US Indian Head nickel dated 1930 is common, coins in average circulated grades sell of $1.00-$3.00
The Denver mint did not issue any nickels in 1906, only Philadelphia did. A 1906 Philadelphia nickel retails at $3 to $25 depending on condition.
In good condition about $2.00
Must be appraised by a professional.
Additional information is necessary to properly value your rifle. There were two models available in the Winchester Model 1906. One had a straight stock and the other had a pistol grip stock and was called a Model 1906 Expert. Which one do you have? Also, you did not say, if your rifle was partially trimmed in nickel or was fully nickel trimmed?
In average condition, it's worth about a dollar.