If the single-speed freewheel is for chains that are 3/32th inch wide, then you should be able to use all types of chains, even chains that 1/8th inch wide.

The critical factor is the pitch, and that is constant for all bicycle chains at half an inch.

However, if the freewheel is designed only for use with chains 1/8th inch wide, then you are limited to 1/8th inch chains. If you try to use 3/32nd width chains, you will find the teeth are too wide for them, and won't engage properly.

You've posted an SS/FG question in the Road forum, so it's a wonder you haven't been flamed like the guy yesterday. Lucky you!