I did exactly the same for my wedding a few years ago now.
But i used standard incandescent bulbs and 15A round pin plug - i plugged it into the venues lighting dimmer rack which meant i could dim the lights to give a nice filament glow. Gave off a lot of heat though!
Consider that 12 X 4W lights will be very bright, i was using 40W incandescence but it was blinding before even 50% power. Maybe get dimmable bulbs and wire to a standard dimmer switch mounted on the back of your letters.
I don't believe you need to cover the flex, as its unlikely to suffer mechanical damage in the short duration it will be used for. However make sure you use strain relief, and clip the cable to be back of your letters.
Make sure your letters are weighted so they don't fall over, consider if children might use them as climbing frames!
Consider the thermal impact, but as you are using LEDs you should be fine.
Wood is a combustible material so i wouldn't want to see any exposed conductors or terminal blocks.
E14 bulbs don't have an earth terminal so only limited PAT testing is possible. I don't know much about PAT but as far as i see it with a E14 fitting all you can do is show polarity (screw should be neutral), L-N & L-PE insulation test and a visual inspection of the installation.