Once again, legal questions vary from country to country and you do not state where you are.
In the USA a signature is generally taken as any mark placed upon the document with the intention of being a signature. It does not even need to be made by the person that the signature belongs to, it can be made by someone else as long as the responsible person affirms it as his signature. This is useful in cases where someone breaks both his wrists for example but still needs to endorse his paycheck.
My advise to you is to simply do what you have planned. If for some reason someone asks you for a "real" paper document rather than a FAXed or electronic one, you can always sign with a pen to satisfy those rare cases.