First thing, get the rear wheel off & measure the distance between the dropouts. If it's 126 you're OK. If it's 120 you're going to have some difficulties. New 27" alloy wheelsets that accept 6 & 7 speed freewheels are readily available. But, most of the brand new 27" alloy wheels w/threads for freewheel come equipped with pressed in bearings. So, it's difficult to change out axle lengths. Go get a cheap caliper from Harbor Freight that's at least 15cm (6in) long & accurate to 0.5mm. Start measuring. Be good. Have fun.