David, Yes- if your airframe was 4 cm (1.57") then you could get away with a fin of minimum "semi-span" of 5 cm (1.97"). That sounds pretty small, but I think some of the Mongoose or Mongoose clone rockets actually have a smaller fin span.
With a long airframe, you don't need much fin area to produce a stable rocket using Rocksim's Barrowman equation. However, be warned that short fins that approach the airframe diameter have very poor lift coefficients, and high angles of attack will not produce the lift you would expect from a fin with a higher aspect ratio. Get too much of a wobble off the rail/rod and you may find it tumbling or taking a short excursion away from vertical.
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