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For plotting small areas, at large scales, and at latitudes accessable to most people, the "poor man's Mercator" you end up with is good enough.  Strictly speaking, "line" CD described should actually curve slightly towards the pole, so that it crosses, say, 38° latitude at an angle of 38°, 39° at 39° and so forth, but the slight error from using the same mile scale for latitudes 1° or 2° away (e.g. at 39° the error is less than 1.5% per 1° of difference in latitude) will be smaller than your errors in dead reckoning.