I'm curious why you don't want to use CRISPR. There are non-CRISPR alternatives that can induce a desired lesion in DNA to promote integration/mutation at the site of interest (engineered Zn-Finger Nucleases, ARCUS nucleases, etc), if that might be preferable. Without such methods, the integration/mutation rate in the clones will be *much* lower
If you want to do it the old-fashion way you could just use some of the pre-CRISPR positive and positive-negative selection tricks (e.g. Diphtheria Toxin & Neomycin) to increase the frequency of correct integration in your clones. You'll need to do a lot more screening.
Article Positive-negative selection gene targeting with the diphther...