I do agree with other here about making connections inside a coil. But I disagree with some of the methods. Holding the two wire ends together and putting solder on the iron then on the wires in not a good connecting method.
You can't reliably 'paint' solder onto a connection.
Also, make a good 'mechanical connection' before you add solder. Then heat the connection and add the solder to the connection, not the iron.
A good mechanical connection of the 'inline' type you are wanting to use is to strip and clean the wire about 1/8 to 1/4 inch using fine (finer the better) emery cloth and not 'across' the wire but 'inline' with it. Then lay the wires side by side and twist them securely.
not like this =
=
===xxxxxxxx
like this______XXXXXX_____
Measure ^ and ^ with the meter.
One wire one way and the other wire the other way, not both ends the same way, then twisted. . .if you can understand that. . .Make the twist as tight as you can without breeaking the wire strand and don't score the wire, if possible. Use your fingers (after a good washing to get the oil out of them) to help keep scoreing to a minimum. Once the connection is twisted securely, check resistance with the lowest setting your meter will do on the ends of the connection (not the ends of the wires). If your connection is open, cut it out and redo it. (open meaning no current will flow from it (the meter will not move)). Once you get a secure mechanical connection, then heat the joint with the iron and then apply the solder to the joint, not the iron. Use a rosin core solder not acid core! Clean off the excess rosin residue with the finest emery you have. Once this connection is finished, borrow the highest quality enamel nail polish the spousal unit has and coat the connection with it. At least 5 layers. Don't allow drips or runs in it, light coats are best. Wait for several hours for it to dry then wind your coils. This will be as reliable as it can get for this type of application and the space compromise will not be too bad with the nail enamel since it will be relatively thin compared to the heatshrink tube.
I said all that to say this, though. . . This is a "desert island" thing as others have said. What you will likely find, though is that your coils will wind with very few of these connections needed. Splicing inside of a coil is not recommended unless absolutely there is no other option.
Doug