Can a shorter IQ test be devised that provides a more approximate measure of IQ?
Yes, what you say is entirely possible. If precision is not as much of an issue, it is possible to devise a test (of anything, not just a test of IQ) which would return a score of, say, 115 plus or minus 10 points. It could also return a yes/no answer to a question such as "is the score inside the range 100..120.

One person who explore such question is Laurencelle, 2015, Le différentiel de sélection multiple [in french] The Quantitative Methods for Psychology, 11(3), 174-188. doi http://dx.doi.org/10.20982/tqmp.11.3.p174