First things first.
A black dwarf is a white dwarf that has cooled down to be in thermal equilibrium of the space around it. It's just a dense lump in thermal equilibrium with it's surroundings. Studying them is pointless if you have already studied white dwarfs because they're just cold white dwarfs - nothing to see here.
So we can skip black dwarfs completely.
A white dwarf can form from almost any star - that is, the vast majority of stars is the Milky Way will become white dwarfs. So these are "easy" to make and messing around with blue dwarfs as an intermediate stage is just pointless farting around. So we just grab any old main sequence star with a mass of no more than about 10 solar masses and fiddle with that to make a white dwarf, right ?
We've already found white dwarfs and why make one when there's already one made for you ?
So we can happily skip the tedious make-your-own-white dwarf step too.
So far, so trivial. :-)
We've already got those so we can again skip the make-your-own stage. In fact we humans have one next door - Proxima Centauri. Maybe your aliens won't be so lucky, but they might even have one in the same system as they live in.
So we're skipping that stage too.
Leaving us with ...
These, as far as we know, do not yet exist.
To "make" one you need a red dwarf of greater than 0.25 solar masses and not more than 0.35 solar masses (the upper limit for red dwarfs). You also need to wait until the red dwarf fuses basically all the Hydrogen in it's core. Then it starts to burn other nuclei and that's when it becomes blue.
And to do this you just wait. A long time. A very long time - something on the order of about a trillion years (compare to the age of the Sun - just 4 billion years).
Start with a lot of helium - enough to make a blue dwarf core (I do not know how much that would be). Introduce it somewhere in "empty" space, ideally directing it towards a common central area.
Add hydrogen ("lots") in a similar way when the central area is reasonably concentrated (but before fusion starts). This should increase the rate of collapse and if you add enough of the right materials you will get a helium core surrounded by a hydrogen body - more or less a blue dwarf. Fusion should start "normally" from gravitational pressure and you can monitor the whole thing to your heart's content.
A few minor details.
To do any of this (including visit existing distant white dwarfs) you need FTL drives. If you can build FTL drives you then have only the "minor" difficultly of being able to transport enough material to make a small star (about 0.25 solar masses of the stuff) to your test site to make your blue dwarf.
The energy requirements for this would seem insane.
However, if you can do all these things then a couple of really difficult problems remain :
- Getting planning permission (good luck because they'll complain about the color not being in keeping with the neighborhood)
- Getting a grant from the science council (low odds, but it's sexy big science so maybe ...)
- Legal objections from the environmentalists.
I'd consider the later one insurmountable.