The fingerprint region is a descriptive name. To actually tell the difference without guessing, you need an IR spectrum taken from known 1-butanol and known 2-butanol.
If you match them up (like fingerprints), then you can tell the difference.
It takes a PhD to be able to tell the difference and even then, that is from repeated exposure, not from some set of empirical rules. IR is a useful but not a very precise analytical technique.
Nevertheless, if you consider that a secondary alcohol has more inductive donation to it from carbon relative to 1-butanol, then you should realize that the secondary alcohol is slightly less acidic than the primary alcohol. If that is the case, the bond between O and H is stronger, shorter and therefore has less stretch. Make sense?