I've messed around with a few methods. You can use butt splice connectors, or wire nuts (not pretty, but they work). And I know you were looking for something other than heat-shrink, but have you thought about using two sizes? One for each wire connection, and another, longer, larger size, to slide over both wires.
Soldering is probably the most sturdy connection, but I can't think of anything other than heat-shrink to cover it up.
As this is an issue I've struggled a lot with - what is the "prettiest" way to connect wires - I'd love to hear an electrician's suggestions.