If your value is not surrounded with quote, then you can put a quote in a cookie value as is.
When NeoLoad detects illegal characters in a cookie value (space, semi column or column), then NeoLoad surrounds the value with quotes.
So, when you have:

myCookie=my value

...then NeoLoad sends in the request:

myCookie="my value"

In this case, you have to escape manually the quote in the value (place \ before the quote).

Example:
myCookie=myValue -> valid
myCookie="myValue" -> valid
myCookie=my"Value -> valid
myCookie="my"Value" -> invalid
myCookie="my\"Value" -> valid