Whether or not a non-compete agreement is enforceable is very fact specific - dependent on many factors, and is state specific, as well. This is an area where it may be worth your while to consult with an attorney in your area with experience in non-compete issues.
While you don't want to end up with an expensive lawsuit on your hands, just because there was a non-compete in your orginal agreement and the company threaten to sue does not mean they have an enforceable legal right to stop you from pursuing your livelihood. An experienced attorney can review all of the circumstances in your situation and determine what the likely outcomes may be under Colorado statutes and Colorado case law. This will provide you with at least a reasonable understanding of the risks and choices goind forward.
It has been my experience that a majority of non-compete agreements are not fully enforceable as the employer believes, and many are not enforceable at all from the inception because they have not bee properly drafted to account for the specific requirements of the jurisdiction. It bears repeating, however, that an analysis must take into accoun all of the facts of the particular situation in light of the jurisdiction's laws.
In Colorado, agreements restricting competition are prohibited by statute, except in certain limited situations. The limited situations in which such agreements may be enforced include non-compete provisions which are included in connection with a contract for the sale of a business or its assets, contracts for the protection of trade secrets, contracts providing for the recovery of the expenses of training, and contracts with executive or management personnel of a company or employees who constitute professional staff to executive and management personnel. This statute applies to employees and independent contractors alike.
I don't know all the facts concerning your situation, but the exception that seems most likely to apply to you (and other independent contractors) is the protection of trade secrets exception. It seems likely that you would have two strong arguments that the non-compete is unenforceable in this situation: 1) It is more broad than necessary to protect the company's trade secrets; and 2) it has expired by its own terms one year after the contract ended. You should definitely seek the advice of a Colorado attorney to help you deal with the situation as it is not a simple situation and full factual analysis is necessary to decide the proper course of action.