It doesn't cost much to hire the facilities at a test house for a couple of hours for preliminary testing, they do that where I used to work. A unit I designed failed on leakage from the RS-232 cables, it just needed a simple filter consisting of a few ferrite beads and capacitors to be incorporated to pass the tests.
1) ensure the PCB with the electronics on it has a good 0V plane underneath the micro, crystal etc. Ideally, lay your PCB out as single sided (often easy with smt) and have the other side as a solid 0V plane.
using a single-sided PCB makes life a lot more difficult, and means you need to pay a lot of attention to the frequency content of every signal. a solid 0V plane allows you to pretty much ignore that stuff.
2) keep fast edges well away from the interconnecting wires and LEDs. If you trace the physical path that LED current flows through, you will find a big loop. Current always flows in loops, and that loop is a radiating antenna, and you specifically dont want that. You have 2 ways to recduce the problem: reduce the size of the loop, and/or reduce the high frequency content of the current flowing in that loop.
In your case the separation between the 2 PCBs and the pin spacing determines the minimum loop size you can have. Your main pcb with a solid 0V plane has essentially zero loop area; if all the LEDs have a common pin, and you make that common (eg Anode +5V) one side of a
2-layer PCB, then the LED pcb also contributes essentially zero loop area, and all thats left is the interconnection between the two pcbs
If you put the LED series resistor on the control pcb, then split it into 2 series resistors, and stick an ~100nF cap to 0V in the middle of them. That will filter out almost all of the HF content, so the LED current will look roughly DC. By doing that you dont really care about the LED current loop anymore, so dont need a 2-sided led pcb.
A similar argument holds for putting an L-C filter between the battery and split-supply chip, to ensure the current that flows in the battery wires is also DC. make sure your L is not a bobbin core (they have a huge external air gap, so convert conducted noise into radiated noise) but is a toroid, little E-core etc. also ensure your LC filter is damped, either with an R-C damper, or a small R = sqrt(L/C) in series with the capacitor.
Then your product will be extremely likely to pass first time.
it is quite feasible to look at the areas of the loops, and the actual currents, and calculate whether or not the device will pass or fail. But you really need to know what you are doing.
In India ? You're joking. Well actually our subcontractor used ETL right next to SEEPZ in Mumbai.
Simplest answer is to approach your test lab and ask about simple 'pre-compliance testing'. I suspect you're going to be most interested in radiated emissions. I'm unsure how you'd test such a device for static discharge immunity but you should ask them.
It pays to buy all the relevant standards btw. I just hope it's not as expensive over there as it is here.