I'm not familiar with your "sip" device, but assuming that it only routes outgoing calls via skype then it presumably has a port or socket into which your ordinary phone is plugged. This should still feed incoming and outgoing voice and fax calls. If you are happy with answering incoming calls then leave the fax machine on "manual" and just press "start" if you hear the tone. If you want fully automatic operation you need a fax and answering machine designed for this arrangement, or a combined phone/fax.
The principle is that the fax listens across the line and only connects if it hears the tone when an incoming call is answered. Otherwise the call is passed to the answering machine or phone as appropriate. To make this work with separate units the fax has to be first in the sequence, and then the answering machine and any phones connected to its output port. The answering machine also needs to be set to answer before the fax, but most of them have a selectable number of rings in the setup menu.
This would achieve what you are trying to do, on one line. Then only downside is having to inform your friends of a change in fax number.
Regards.