Reduce RF noise from a DC inverter
I suspect your problem is not exactly what you think it is. It's true that your driver is producing wide-spectrum RF noise, but putting it in an enclosure isn't going to help. And filtering the inputs won't help either. 

Your problem (I suspect) is that your EL wires, being driven by more-or-less square waves, are acting as transmitting antennas, and as long as the drive is wideband you'll be getting interference with your RF.

There are two obvious solutions, but one underlying problem - high-frequency RF generation.

1) You can use your inverter, but put its output through a low-pass filter of, say, 10 kHz. The trick will be to use a low-pass filter which has really excellent performance at high frequencies, and this is tougher than you might think. A 10 kHz filter will not ordinarily be tightly specified at frequencies more than 2 or 3 orders of magnitude above its critical frequency.

Alternatively, you can run it through an RF low-pass filter with a cutoff of, say, 1 to 10 MHz, and hope that your GHz levels are low enough.

In either case, you'll need to see about making a proper enclosure for your inverter.

2) Since EL wires don't normally take a lot of power, finesse the whole problem by driving them with a sine wave in the first place. Build a simple 3 kHz or so sine-wave oscillator, add a power stage, then run through a step-up transformer such as a vacuum tube coupling transformer to the voltages you need (typically a few hundred volts). While this will obviously require a heavier transformer, it may not be as bad as you think. First, I'd expect a power level of only a few watts, so the transformer can be (relatively) small. Second, there is no need for careful shielding and filters, so you save weight there. Whether the tradeoff would work or not I really don't know, but you might look into it.

EDIT - As to components, I'm not entirely certain. For a simple filter it might be possible simply to use an inductor such as an RF choke. Your current levels are low, and the EL wire has considerable capacitance all on its own.  The thing to watch out for is voltage rating, since ELs typically require several hundred volts.

As for making an oscillator, see the Texas Instruments AN-263 (Google on "AN-263) for a wide variety of oscillator approaches. The easiest way to make a power booster is just to use any audio power amplifier chip that will put out a few watts. 

Transformers would just take too long to explain here. Suffice it to say, to get from 10 volts out of an amplifier to 300 volts at the EL, you'll need a voltage ratio of 30 to 1. Audio transformers are spec'ed in impedance ratios, which are the square of the voltage ratios. I'd suggest two transformers in tandem, each with an impedance ratio of 30:1, such as 8 ohms to 250 ohms.