Again, welcome to design....
Does the heatshrink conduct as good or better... etc?
It'll probably be fine.
Or maybe heatshrink isn't needed. I often don't for grounded ends, or resistor junctions, or resistor-LED junctions - but that is based on those junctions not causing damage to other circuitry (ie, low or no current through resistors, LED or gnd) as opposed to OTHER conductors hitting them (and thus doing damage).
But I have learned that it doesn't matter that nothing can ever hit an exposed conductor because eventually something will. (I should have learnt from telcos - even when their DC bussbars go through inaccessible areas, the are still covered with insulation. Not that their bussbars are fused, but often neither are our exposed circuits in terms of NOT damaging surrounding circuitry.)
Of late, I have tended to wrap (heatshrink) whether needed or not, though often this had been to increase joint strength for flying leads etc.
Besides, if your resistors get too hot, you'll probably smell the heatshrink - ie, get a warning.
And if they do overheat, they should go higher resistance. If they do blow, they should blow open - ie, a circuit failure but non-destructive (other than the resistor, and the burning Aurora (Borealis?))
The 560R (1/2W, else 1/4W) should be fine. That should give max intensity and be ok for a supply up to 14.8V shown before.
If your system goes higher than 14.8V (as some do) - but at the LED source - and if those LEDs thus destruct, you can increase the resistor. 680R is the next size, then 820R.
That means lower intensity but it may still be sufficient for your needs. You might find you want bigger resistors anyhow if they are too bright. (And at 680R and above, 1/4W should be fine: P = iiR = i x i x R; or (VxV)/R.)
Post-Edit: Most readers should stop here... The rest has little value-add. Maybe.
Funny how this thread reminds me so much of another.....
The other thread gave the following link for these
OSRAM HyperPointLEDs (pdf; 643kB). I liked the datasheet because it showed so many aspects of LED behavior. (It also blew several of the thread's
arguments out of the water. I like people that supply their own rope!)
A lot of the info is batch & physical stuff, but some diagrams illustrate color, intensity, current, voltage etc shifts with temperature/current etc.
Its CIE "color" diagram may be a bit confusing. Essentially it is a 3D "color map" drawn in 2 dimensions, but essentially it covers all visible colors and assigns coordinates (u,v or Cx,Cy) so that any color can be defined.
(Manufacturers and Standards use them - eg, one Standard (ISO-whatever part 17?) states that for colour redundancy (discrimination), the different colors used must be separated by (u,v) > 0.2 (or something similar...) - it's all fabulous stuff except when moron managers start specifying those standards for OH&S reasons yet have no idea of the implications nor implementation, but I'm not one to whinge!)
Oops - I digressed.
Anyhow, flick through the pdf and look at some of the graphs.
In many ways it shows why approximations are ok, or aka near enough is close enough (aka some implement extreme pedantics for no reason, but at the expense of reliability and serviceablity).
But again - try/test and see.
If >560R is okay, use that for more margin. (ie, 680R, 820R, 1k etc)
Do they work okay under dimming?
Feel the heat from the resistors.
[Note that a LED-free resistor on 14.4V dissipates nearly 50% more power than at 12V - ie, P in a resistor = VxV/R, so P is proportional to voltage-squared. P@14.4 compared to 12 = (14.4 x 14.4)/(12 x 12) = 1.44 = 44% more heat. That's a principle I've tried to knock into a few local audiophiles with under-rated alternators and poor SMPS (dc-dc converters) in their amps - ie, for normal amps (45-200W per channel), the amp at 14.4V will put out 44% more power than at 12V (usually more, but it all depends...).]
Isn't it good that with all the things that can go wrong, you can get a $15 replacement? That's about $985 to spend on other projects - maybe a holographic heads up display (direct projection - not crappy 3D windscreen stuff) - then you scrap all illumination etc except for the projector (and I prefer synaptic injection rather than retinal - electro-mag is still more efficient than optic for modern transducers).
But let's make sure you close this project first.
Yep - I definitely need a cool soak soon!