I've never built anything in 1/200, but I've done lot of portholes in 1/700 which I assume is no more forgiving.
Typically I'll mark out the horizontal centerline with some type of hard edge tape
https://www.amazon.com//dp/B00B8GQRHK ( or Dymo tape, scribing tape, even masking tape sometimes) and then mark the centers with a needle tool of some type
https://www.amazon.com//dp/B0028MV9G2 to center the drill bit before drilling with a pin vice.
Links above are similar to what I use, but not necessarily specific recommendations.
Related - I'm really
not much of a fan of the newer drill sets with tungsten carbide bits.
https://www.amazon.com//dp/B07G6STHKW I can't even keep one on the desk top without the bit breaking. Strongly prefer regular old carbon steel bits for smaller sizes.