+1 on the relay. I too am working on an Austin Healey replica (Sebring) and I can say that the original wiring was minimal. As I recall, the main supply to the harness is just 10 gauge wire (maybe 12 gauge) and this has to carry all the loads in the car. As these cars were built mostly back in the 80's and 90's, they were not really wired with electric cooling fans in mind. I will be rewiring mine with my own harness.

A 20 amp draw with a 90 amp supply shouldn't cause major problems provided the wiring is up to the task.

Run a separate wire with 30 amp fuse directly from the battery to the switched portion of the relay. This should be 12 gauge at a minimum, 10 gauge would be better to minimize voltage drop. The relay coil would be triggered by whatever switch you are using now. The fan ground would be better if run to the engine block or directly to the battery.

You didn't say if your car is a new build or a rebuild of an older car. If it's a rebuild, I would recommend that you look at the whole wiring harness carefully. It could have many poor or deteriorated connections in the harness (mine did). There are many street rod wiring harnesses available now that will have better wire, modern fuses and are built with things like fans in mind.