Bulk renaming organizations tags

I am trying to rename a couple tags in hundreds of organizations.  Knowing that there is no easy API for this job, is the easiest way to handle this is to add a new tag to all of these organizations and then delete the old tag?

I have the following python script prepared with issue finding the organizations with the tag:

#!/usr/bin/python

import sys
import json
import requests
import getpass

sys.stderr.write("Zendesk email: ")
zd_username = raw_input()
zd_password = getpass.getpass('Zendesk password: ')

orgIds = set()

url = "https://mycompany.zendesk.com/api/v2/organizations.json"
while url:
    r = requests.get(url, auth=(zd_username, zd_password))
    if r.status_code != 200:
        print ("Error: login failed")
        exit(1)
    print("Reading %s ..." % url)
    respond = r.json()
    for org in respond["organizations"]:
        if org['tags'] == 'old_tag':
            orgIds.add(org["id"])
    url = respond["next_page"]

for id in orgIds:
    print("Updating %d..." % id);
    r = requests.put("https://mycompany.zendesk.com/api/v2/organizations/%d/tags.json" % id, auth=(zd_username, zd_password),
            headers={'Content-type': 'application/json'},
            data=json.dumps({"tags" : ["new_tag"]}))
    print(r.status_code, r.reason)

Any help is appreciated.