Need advice on connecting Macbook Air to HP all-in-one box (Thunderbolt 2 to Thunderbolt 4, I think) My daughter has a non-most-recent Macbook Air with what I thought was originally a mini-DP output but it turns out to be a Thunderbolt (probably v2 since the Mac is only a couple of years old). This particular model seems to have {audio out, USB-A, power} on the left, {SD (I think), USB-A, Thunderbolt 2} on the right (both listed front to back).
We want to use one of our existing monitors hooked up to another of our systems, without having to remove and re-insert cables all the time.
This monitor is fed via HDMI from a HP Thunderbolt dock (HSN-IX02) which only has a Thunderbolt/USB-C input, but many other outputs (HDMI, DP, etc). The monitor has HDMI, DVI and DSUB inputs of which the first two are in use.
I very foolishly bought a mini-DP-to-DP cable, thinking that would work just be plugging the Mac mini-DP output into the dock DP output, not realising at the time that:

the latter was an output rather than an input; and
the Mac output wasn't even a mini-DP :-)

So I think what I need is a cable with male Thunderbolt 2 at the Mac end and female Thunderbolt/USB-C at the dock end (the dock has a hard-wired input cable with male Thunderbolt/USB-C).
My concern is that all the cables I look at seem to assume the Thunderbolt/USB-C is at the Mac end (which is true for more recent models) and I don't want to blow more money on the wrong cable. In any case, the Thunderbolt/USB-C end for these cables is male and I need female.
So I guess my question is: will such a cable work from Thunderbolt-2 at the MAC to Thunderbolt/USB-C at the other end? I assume I will also need to purchase a female-female gender-bender to connect at the dock end as it's the wrong gender.
A secondary question is: what are my other options, if any, for external displays on this Mac? There appears to be no other output ports and I'd rather not have to buy another monitor since we have no place to put it.
First: Your Macs Thunderbolt 2 (TB2) port can act like a mini-DP port, so any cable that is mini-DP to something that can be connected to your monitor will work. However, connecting your TB2 MacBook to that docking station will most likely not work and may be expensive.
You mentioned there is a free VGA port on your monitor, so I would get a miniDP to VGA cable. Inexpensive and should serve your needs. However, as Gilby has pointed out in the comments this will usually limit your resolution to 1920x1200.