I use electrical tape. Always carry a role with me when I'm flying mics. Its nice because it won't leave the sticky residue that duct tape can leave sometimes. I mount my mics on my stand first, then put the umbrella on. This will ensure that your umbrella isn't going to be in the way of the mics/cables.
Here is the umbrella I use. I bought it at Dick's Sporting Goods. You can find them online too. Do a search for "Drizzle Stick." I like it because it has a small radius and is kinda deep. It is less prone to catching wind than other umbrellas i've used in the past.