There should be no problem swapping for an LED bulb. Remember the LEDs produce very little heat, so you should be able to 'manipulate' it into the space.
You can get little bulb holders as well which might make fitting easier. Here is what I use:-
View attachment 109172
Bulbs
Holders
These bulbs are only 1.2W, equivalent to 10W, so you might want to get a higher output. Note also LEDs are available in different colour temperatures. 3000K up to 6500K the 6500K bulbs are called 'daylight', very white light and sometimes not comfortable to work under, the lower colour temperatures give a warmer light, which may suit a kitchen better.
Possible issues: the old incandescent bulbs will have been supplied with 12V AC generated by either a traditional transformer or an electronic transformer. A traditional transformer is a lump of metal on a bracket. An electronic transformer will be in a plastic enclosure . The traditional transformer should work OK, however some electronic transformers need a minimum load to operate correctly and often the LED bulb will be below the minimum load. This is easy to overcome by adding some appropriately rated resistor to the circuit. The best way is to try it and see.
LED bulbs have a basic regulator inside operating at high frequency, so they can cause horrendous mains conducted and radiated noise.
A bit for information: The LEDs I use (above) are designed for 12V ac, but since they have a full wave rectifier on the input, they will operate with 12V DC and not polarity sensitive. There may be a slight drop in light output with DC.
LED fittings can be either constant current driven or constant voltage. It depends on the design. The basic LED device requires a constant current, but that is easily achieved by using a series resistor and feeding the circuit with a constant voltage. High output white LED's drop about 3V across them when running, and about 1.2A (approx),