HA tyres replacement

[HC]

I am thinking to refurbish my 12'' steel wheels on my HA. fitted with 155/80/R12, I was wondering if I can replace tyres dimensions with 165/60/R12.
Does 165 width fits onto the original Steel rims? Do they rub to the inside on full steering lock?
Does a 60 profile compared to those I currently have (80) looks strange under the arches? I know the ride height and comfortableness will be altered.
Any advice will be great
& Regards
Chris