Separation of smaller DNA fragments and larger fragments without using gel electrophoresis?
One option is to use SPRI beads, like those sold by Ampure (Ampure XP beads) to separate DNA fragments by size. By adjusting the ratio of beads to sample, you can selectively bind fragments of certain lengths by excluding those of other lengths, as seen in the following image: 


From this image, you might try using a beads-to-sample ratio of 0.7 to exclude fragments below 200bp, or a ratio between 0.7 and 0.6 to exclude only those fragments below somewhere between 200 and 250bp. The advantage to beads over a gel is the time it takes. Size selection by beads takes only around 10 minutes, versus maybe 30 minutes or more for a gel (including the extraction). 

As with any molecular biology procedure, it's important to test it and make sure that it works for you. For instance, it might be a good idea to take aliquots of your samples and compare the lengths and yields that you get from a range of bead concentrations and/or to compare the yields that you get from using gel vs (in this case) beads.