As long as your new insurance will kick in within the 60 day window you have to elect to sign up for COBRA insurance, there is no need to sign up for COBRA insurance.   The reason for this is that you elect to sign to sign up for COBRA insurance on the 60th day, your health insurance will be retroactive until the last day of your employment.   That means that if for any reason you got sick  or needed medical attention during the 60 days, you could then just pay the premium and be covered for those expenses.  If you don’t end up needing medical attention in those 60 days then you didn’t waste the money paying for  the two months of premiums.  Essentially, you would actually never be without coverage, since you can activate it at any time within the 6o days and cover the full term.

Your other option would be to sign up for a short term health insurance plan, which can be anyway from 1 day to 1 year, at a much cheaper rate than COBRA.  This would cover you for any major medical costs.