Can't help with the dropper. Do be aware that any liquids can leak and cause issues with the rest of your kit. Especially something like iodine, which is pretty reactive.
I've stopped carrying bottled iodine after one leaked in my first aid kit and ruined everything inside. It was tightly sealed and wrapped in plastic wrap.
...The Sawyer Mini is inexpensive and effective when used properly (NB don't expose it to freezing temps after its been used, and it doesn't work against viruses).
If you need to use chemical disinfection I would strongly recommend chlorine dioxide tablets -- I carry them as a backup. Iodine doesn't take care of cryptosporidium, whereas chlorine dioxide will if used correctly...
I agree with Choasmagnet on both points. Sawyer filters are easy to use and will treat a practically limitless supply of water as long as you back flush it occasionally. The Sawyer Squeeze has a faster flow rate for an ounce more weight.
As a backup, or if you are traveling to an area that you have to worry about viruses, than the chlorine dioxide tablets will treat more pathogens than iodine. I keep some in my PSK and my wallet. They take up little room and weigh almost nothing.
if you really prefer iodine for water purification than I would suggest carrying it in pill form for the reasons mentioned above.
I do carry some iodine pads for disinfecting wounds and you could also use them in a pinch by squeezing out drops into your water container. I've had a DEET pad develop a tear and ruin my first aid kit for a second time, lucky I guess

, so I keep all strong pads in tiny Ziploc bags to protect my other gear.
Good luck with whatever method you decide to use.