There are actually several more options that you have in order to get rid of the eye caps and prevent/treat infection of the eyes (as well as suffocate any mites that might still be present without showing themselves):
Most common procedure to prevent/treat infection of eyes is terramycin ophthalmic ointment (available at Rural King, TSC, etc. in the cattle health aisle, unless you are living in CA). The product is applied directly to the eyes once. After three days use a cotton swab and slowly roll it against the edge of the stuck cap until you can get a hold of it.

If no mites and no infection (swelling would indicate an infection) is present use mineral oil (Kroger, Walmart, Walgreens, etc., in the shelf with laxatives). The most common brand is Roberts. Do not use baby oil!!! Use a cotton swab to apply liberally to the eye caps. After approx. an hour use a cotton swab and roll it against the edge of the stuck cap until you can get a hold of it. If it doesn't come loose, reapply mineral oil, wait another hour and dab excess from the eye cap using a clean piece of paper towel. Wrap a piece of artist tape (masking tape will do too) - sticky side out - around your finger and gently but quickly dab the sticky side onto the stuck eye cap.