user2555451's answer is spot on, but just as an observation on how to get these into Python efficiently - the first part of your question - try this:

symbols = set(r"""`~!@#$%^&*()_-+={[}}|\:;"'<,>.?/""")

That:

1. Wraps the string in three quotes to simplify handling the single or double quote issue
2. Puts an r in front of the string to handle the escape character
3. set converts the string to a set

The initial string was missing the close square bracket, just as an aside. Using a simple set operator:

>>> symbols - set(string.punctuation)
{']'}

There's no built-in function, but you can always build one.

This function checks user input for illegal characters (for naming files in Windows), cuts them out, notifies user and asks whether to submit a corrected string.

def infinite_char_check(string):
    """
    Check string against exclusion list, correct and ask to submit.

    Parameters
    ----------
    string : str

    Returns
    -------
    string : str
    """
    punctuation = ["|", "/", "\\", ":", "*", "?", '"', "<", ">"]
    the_same = string
    for symb in punctuation:
        string = string.replace(symb, "")
    if string != the_same:
        print()
        print(
            "Illegal characters detected! "
            'Please avoid using this set: /,\\,:,*,?,",<,>,|'
        )
        print("Corrected string: ", string)
        print(
            'Input "Y" (or "y") if you\'d like to change it, '
            "otherwise input any string"
        )
        spchk = input()
        if spchk in ("y", "Y"):
            print("Input experiment name")
            new_name = input()
            string = infinite_char_check(new_name)
    return string