Independent contractors are free to contract -- California employment law does control where the parties are true independent contractors. Even were you determined to be an employee, there is little to prevent an employer from making requirements concerning computer usage.
As for you being required to sign the contracts -- no, you're not required. And, the contracting party is not required to hire you -- which is almost certainly what will happen if you don't sign.
So, nuts or not, you're probably stuck. Though, as a practical matter, these types of contracts are rarely sued on, unless the breach is so damaging that the contracting party's business is destroyed in the geographic area. Thus, you may be overthinking your risk.
Hope this helps.
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