Some of the chemicals involved can be absorbed through the skin, but you're not likely to be exposed to great enough amounts to pose a danger other than a possible allergic reaction and skin rash.
Nor would the fumes be a problem if you were just visiting the shop as a customer.
The few studies that have looked at pregnancy among cosmetologists have shown mixed results: One study suggested an increased risk for miscarriage among cosmetologists, but several other studies found no additional risk.
It's not clear how to reconcile the differing results.
The studies didn't differentiate between women who work with hair care products and those working with nail products, so even if there is a hazard for workers, it's not clear whether it's from hair care or from artificial nails work.