sed command

[masalachol]

I have a file where I have to remove the commas that are between quotation marks and then replace the quatation marks with a pipe |. ie

so far I have sed 's/\("*[,]*"\)/\|/g' and this replaces the quotation marks with a | but I feel I am going about it the wrong way. Any suggestions?

file
"Hello, World"
"Hello World,"
"Hel, lo World"

result

|Hello World|
|Hello World|
|Hello World|

Regards,
Milenko