According to this table:
American Wire Gauge table and AWG Electrical Current Load Limits with skin depth frequencies and wire breaking strength
For 10KHz the maximum conductor size would be AWG16 or 1.3mm, so that would be 4 strands
For 100Khz it would be AWG26 or 0.40mm, 41 strands. At this point makes sense to get the litz wire, doing it manually would yield a very large diameter conductor.