If you replace the originals with halogens of similar wattage the wiring will be fine and won't notice the difference, you will simply get a higher light output. It is only if you use high wattage ones that your wiring might struggle. What halogens do you have in mind?
Will the wiring and fuses in my 1998 Road King hand Halogen Spot Light Lamps? Or is the wiring too small to handle the amperage?
The stock Harley passing lamps are sealed beam units for a 1998 Road King Classic.
I believe it is part number 68674-69 for the sealed beam and are 25 watts each.
If you decide to substitute another 4.5 inch light then each light should be of the same or similar wattage rating.
Consider review of wire connection at rear of stock sealed beam when ordering a substitute in order to facilitate connection.
I had Harley halogen lamps with H3 bulbs for a few years which were a big improvement over the stock sealed beams, but replaced them with LEDs two years ago. Just as bright and a lot less current draw.