Who is the professional you are talking about to do the soldering?
Obviously it won't be the ficticious HVAC tech you made up, so it will
probably be you.
Yes, it can be done, depending on how much wire there is to work with,
if you know how to solder, and insulate a connection. There are also
other ways to extend wires without solder that are equally if not more
FYI, there is a more than fair chance you have damaged your furnace by
powering up with bare wires not connected to a thermostat, and
therefore, more than likely connected to each other.
I'd recommend you call a real tech, and have him do the work, and then
be done with it. You are well over your head here.