tiny conductor = high impedance
No. Tiny conductor = higher resistance from one end of the conductor to another. You are confusing conductor resistance with cable impedance.
If you look up cable characteristic impedance you will see that that in a coaxial cable, it's impedance is determined by the diameter of the conductors in relation to each other.
A coaxial instrument cable that has a 20 gauge center conductor can exhibit the same characteristic impedance as a coax that has a center conductor of 5/8" OD. We all know that a 20 gauge piece of wire will have a lot more resistance per foot than a 5/8" in diameter copper pipe. I have at my disposal, and work with as a part of my day job both of these types of line. They both have a characteristic impedance of 50 Ohms. I could and do, use the smaller cable to make instrument cables at work and for my bass guitar use. And as long as you don't exceed the current rating of the center conductor (20 gauge = 5 amps) you can use this for speaker cable. In fact how many speaker cables have you seen in low to moderate power systems that used an instrument cable with RCA connectors for speaker connections.
Typical instrument cable can have a characteristic impedance of 75 Ohms and lets say it has a conductor size of 26 ga. That means it can carry 1 amp of current and will work for low power speaker systems. 50 or 75 or 100 Ohms impedance makes no difference. Zip cord, aka lamp cord, is often used for speakers and it has a characteristic impedance about the same as 75 Ohm instrument cable. It's not about cable impedance. It is about current carrying capacity when it comes to driving speakers.
Characteristic impedance is not an issue at audio frequencies in spite of what some self professed audio gurus may believe. Look at what happens when you daisy chain two speaker cables. Say you have a six ft, 75 Ohm cable connecting a head to to a cab. Then you have another 6 ft, 75 Ohm cable connecting the first cab to the second cab.
What happens to the cable impedance when you add two 75 Ohm cables of equal length together to make a 12 ft cable? The resistance doubles but the Characteristic impedance stays the same.
Look at any set of cable specs that includes impedance. The impedance rating of the cable is not given in Impedance per foot. It is a fixed number based on how the cable is made. What you will see is a DC resistance number that is per foot (or meter). The total DC resistance increases with length. The impedance stays the same regardless of length.
I have built both parallel conductor (zip cord type - 300 and 600 Ohm) and coaxial lines (50 Ohms) that needed to be these certain impedance to work properly. In coax, there is a formula that uses the ratio of the diameter of the center conductor to the outer conductor. For parallel conductor (zip cord) the main consideration is the spacing. The DC resistance of the conductors does not figure into the cable's characteristic impedance.
Get inside of a speaker cab. The conductors may be inches apart and or right next to each other or any combination. That particular arrangement will exhibit some unknown, but measurable impedance. If impedance of speaker cables were important (it isn't because it is audio) then what is inside the cabs would be very tightly controlled as is done with instrument cable. Cable impedance is just not important in connecting speakers.