For a bazooka balun, you want the $Z_0$ of the transmission line to be as high as possible. A thin layer of heat shrink is not ideal.
If you must use a sleeve balun for mechanical reasons, rather use a 30 mm diameter pipe with the coax inside it.
The impedance of a short circuited transmission line is
$Z_{SC} =jZ_0\tan(\beta x)$ where $\beta=2\pi/\lambda$
At a quarter wave this is an open circuit, but at any frequency away from a quarter wave, the impedance drops quickly and the line $Z_0$ matters a lot.
If the frequency changes by 10%, (or you get the velocity factor of the line wrong by 10%, very likely if you don't know the dielectric well, or measure it), then the impedance is $j6Z_0$. If your line $Z_0$ is $25\space\Omega$, that's only $150\space\Omega$, not a very good choking impedance. If you make a $120\space\Omega$ two wire line with a second piece of coax taped against the feed, it could be almost $1000\space\Omega$ at the same frequency offset.
So I suggest a kind of pitch fork of two parallel wires, a quarter wave long, one each side for symmetry, spaced about one coax diameter apart. Braids soldered together at the short circuit side, don't worry about the inners. No need to remove the jackets.
Like this, if you're using the outside of the bazooka as a dipole element (diameters and widths exaggerated a lot):

Or like this if you need a balun for a balanced antenna like a dipole:

Finally, you don't know the RF properties of the plastic and glue in the heat shrink. You can compare it to the coax jacket by putting a piece of both in a microwave oven, with a small glass of water on the far side. Cook them for a bit and see which plastic gets hot first. A good dielectric like PTFE or PE won't get hot at all.
It's a great idea to build and measure these things. The way to test for unbalanced currents is to mount the antenna say 2 or 3 metres high on a wooden pole, and watch the VSWR display while you run your hand down coax. If the graph jumps around then there are currents on the coax. Be sure to evaluate the whole frequency range you're interested in. At slightly higher frequencies, I remember seeing the trace dancing around in most of the graph, and being stable in the middle where the balun was working.