By waiting for a month, you mean just letting the account rot for a month or actually playing legit on it? Jagex has logs of your logged in activity, if you just "wait to avoid delayed bans", that's not going to help you at all, as no new entries are added to the account logs. You may as well bot shrimps for 3 hours, let the account rest for 2 years and log on it, you are very likely to get banned.