Instead of getting insurance you can cover the costs out of pocket. I e. If you had 6 months of expenses saved up you could afford to go without short term disability, because you've already got the money saved.
Life insurance is usually held to cover funeral expenses at a minimum, and replace someone's income for their spouse and/or children at higher levels. At 60, I would think you'd be close enough to retirement that your assets would be such that you wouldn't need a big payout for your dependants.