I believe that to generate the .stl file you need to have a closed solid. If you are making a miniature version, can you leave off some of the small fillets? You may find it easier to delete those surfaces, then fill the holes in with a fill or boundary surface.
If this is a small part to fit on a key chain, I don't think FDM is the best choice, as you can't get very fine detail.
Well, it depends on if you want gaps in your FDM model or not. The stl file and FDM printer won't care if there's gaps, the printer may just fill it in with support material.
If you just want a simplified model, and no gaps, re-modeling it may be faster than fixing all the gaps.
Do you have access to the ProE file or the creator? If it is a solid there it should be easy for them to save it out. Basically you are working with a bad model.
If not you could try posting your file and we can probably offer better advice. I hope this helps.
Are you using Solidworks 2010? With 2010, you can change the knit tolerance, so you can set it higher.I assume if you can get it to knit, it will produce a good .stl file. Conversely, just setting a high knit tolerance for exporting in IGS or STEP may just produce faulty gaps.
Try fixing some of the gaps with some of the surfacing tools, and then seeing if changing the knit tolerance will fix the others.. Try Delete Face using the "Delete and Patch" option turned on. How many gaps are there?