I don't know where this myth that stainless steels are non-magnetic comes from.
There are three basic types of stainless steels. All stainless steels are normal steel with some chromium and/or nickel added to increase there corrosion. Of the three basic types there are:
Ferritic stainless which is magnetic, non-hardenable and easy to machine
Martensitic stainless which is magnetic, heat treatable, enhanced strength and relatively easy to machine
Austenitic stainless which is non-magnetic, very hard and strong, far more difficult to machine but has high corrosion resistance.
Some type numbers:
Ferritic 430 & 430F
Martensitic 410, 416, EN56, EN61, EN62 & EN57
Austenitic 303, 304, 316, EN58, EN58A, EN58B, 440 & 440F
As well as chromium and nickel additions some types have niobium and titanium to modify the characteristics.
Generally to be classed as a stainless steel the alloy must include at least 10% chromium. Also note that stainless steel is exactly what its name suggests, it is resistant to staining by chemicals, it is not necessarily rustless or resistant to corrosion. Some grades of classic stainless steel do in fact corrode when sea water or other mild chemicals are present. A common use of 316 steel is battery clamping bolts which has the highest corrosion resistance, but 316 has a lower tensile strength than other types. 316 compared to a normal high tensile bolt is only about 40% of the tensile strength, so care needs to be used when critical applications are encountered!
Surgical scalpels and other cutting tools such as knives are traditionally made from 410 as it is heat treatable to harden the edges.