cold water pipe condensation

yes

yes, use a final impervious wrapping to prevent moisture gettin to pipe

(I was worried about trapping

No, insulation + vapour barrier.

Normally here split foam slipped over and then the whole taped up with gaffer tape. (duct tape/Duck Tape

You want closed-cell insulation. It's used for cold refrigerant and chilled water pipe insulation in air conditioning systems. The closed cells prevent the insulation becoming water-logged and no longer acting as an insulator. Armaflex is the best known make.

Having said that, the cheap grey pipe insulation for heating pipes seems to be sufficiently closed cell to work for what you want.

You could try changing the water pipe to plastic

That's what we have, and it still had lots of condensation until I added insulation and tape.

Armaflex Self Seal Pipe Insulation.

- Foamed Nitrile Rubber (Closed Cell)

- Built in Vapour Barrier

- minus 50oc to plus 105oC

- Class 0 fire resistance (self extinguishing, no drip)

- Self-Seal is pre-slit with already applied double sided taped on each slit surface

- Thermal conductivity @ 0oC = 0.034 W/mK

- NOT for outdoor use re UV protection unless Armafinish FR paint applied within 3 days & 2 or more coats may be required

You can also buy it plain slitted and you need glue.

If you needed more insulation you could use the Celotex/Kingspan "version", it has a foil inner & outer covering. I think that is more for steam heating pipes, never looked into it.

Should be available in the USA re HVAC (air-con) suppliers. Just check it is fire retardant re plumbers torches & electrical.