Danielle, if you can write to a spreadsheet, and then save the spreadsheet as csv, you'll get what you're looking for. Whether or not you can do that depends on what p[latform and version you're using.
You can't just "delete" the NaNs from a numeric variable, you'd have to convert to a cell array and replace cells containing NaN with empty, and you definately don't want to do that if you have a lot of data. You could however follow the lead of data analysts of days past, before NaN was a standard, and replace NaNs with something like -99 (or some other "impossible" value), save, load into Stata, and then deal with the -99's.
Hope this helps.