I would advise that you treat the payment for your shared workspace as "Rent" on the Schedule C for the self-employment income from your Form 1099-MISC.
For more information, please see IRS Pub. 535 Business Expenses.
I am thinking about joining a local coworking space. They offer options where you can buy a 2, 4, or 8 day pass for each month. I would hold meetings and also just work from there. Am I at risk at losing my home office deduction?
Simple answer: no. Your home office does not have to be you only place of business, but it must be your principal place of business.
Regardless of the method chosen, there are two basic requirements for your home to qualify as a deduction:
You must regularly use part of your home exclusively for conducting business. For example, if you use an extra room to run your business, you can take a home office deduction for that extra room. Exclusive means you do not also use the space for personal use. Exclusive does not mean it's you only business space.
You must show that you use your home as your principal place of business. If you conduct business at a location outside of your home, but also use your home substantially and regularly to conduct business, you may qualify for a home office deduction. http://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Home-Office-Deduction
But, taxes aren't simple. So, maybe the ITS would question you having both a home office and deducting rent for co-space. You should keep a log of where you work.