The words in the Museum register on the "Oswald" line appear to be written by a feminine hand.
Near to it are others from Texas. Maybe a group of teens went there and one of them had written a school paper on detectors. "Dallas Rd" means the person had no idea where the real Oswald was currently living.
The "l" in "Oswald" is usually developed in other samples by Oswald, but the Museum "Oswald" looks more like "Osward". The other "l"s (as in "Dallas") show the writer knew how to write a "l" properly. It may be that the writer couldn't quite remember how to spell "Oswald".
Oswald wrote his capital "D"s quite different compared to the Museum writing. The "e"s in "Lee" are closed in the Museum writing, while Oswald typically had open "e"s.