In addition to Randall Grubb, John and Gertrude Gentile also used a signature cane with a G in it. Robert Grablow, of course, used the RG signature cane.
Also, Perthshire used letter canes for its PP14 and PP32 paperweights. In the case of a letter G cane, that would have been a PP14 from 1975. The PP14 used every letter over the course of the years it was made; A for 1969 through Z in 1994. There are no other factory designating signatures in these weights - no letter P for Perthshire. Of course, in 1984, in the alphabet sequence, the P was used.
The PP32 used J through R from 1978 to 1986.
Can you post a photo of the weight? I'm sure we'd all like to see it.