In gel filtration chromatography (GFC), you must dissolve your sample in a "good" solvent. But your sample must also be soluble in the mobile phase. The best method is to dissolved your sample in the actual mobile phase that you are using. You are correct that the sample may precipitate in a different solvent. To check this, dilute some of the sample with mobile phase and watch for the solution to become cloudy. It may take a few minutes. However, usually your sample solution is not very concentrated, and at dilute concentrations it will be soluble even in mobile phase. But there is no problem with using a detergent in the mobile phase. Visit the website for the column manufacturer, and look for GFC applications of proteins. There are many other ways to do this separation.
Also, I hope you realize that GFC is not a high resolution technique. Very small changes in molecular weight will not be noticed. You must choose your column carefully so that it can separate molecules in the size range where you want to see differences.
Good luck!