Fran - our company never had an insect repellant product, so I was never asked to assay for DEET.
However, I typically do not like HPLC procedures with low absorbance wavelengths like 220nm, especially for products such as these that contain DEET at relatively high levels. I searched DEET structure, it has an aromatic ring, likely has absorbance higher than 250nm which would give much better selectivity compared to product matrix components.
If me, I'd dissolve pure DEET in solvent, and run UV scan (or even HPLC DAD scan) and pick a higher wavelength for better selectivity. I see online a procedure using 254nm, that sounds much better, but whenever I see "254nm" I wonder if someone had only an outdated single-wavelength UV detector available!!!
http://www.bmsw.net.cn/EN/abstract/abstract10604.shtml
To extract from a cream base, I would try DMF and I would try methanol as first choices, but first try DEET in those to check on its solubility. If DEET dissolves in a solvent, and the finished product dissolves readily or disperses readily in that same solvent, you're most of the way there. Keep injection volume small (5 microliters or less) if injecting that organic solvent extract into a mobile phase high in aqueous.
Start with RP-18 and try to keep the procedure isocratic for simplicity if you can. My guess is that this assay should not be too challenging.