Options for impacted canine teeth without braces?

Canine impaction is one of the most common permanent non-wisdom teeth to be impacted. As you noted, the traditional way to treat this is by exposing the canines, putting a button/chain on them, and then drawing them down into alignment with orthodontics. If your teeth are otherwise in perfect alignment, you may not require full orthodontics to draw the canines into alignment. Consult with an orthodontist. It may be possible to create space for the permanent canines with Invisalign, and then draw the canine into alignment by limited use of conventional orthodontic wires. Your thoughts about extracting all the canines and placing implants would not be a viable alternative. The amount of palatal bone removal required to extract your permanent canines would be excessive and would unnecessarily compromise your bone structure requiring bone grafting to replace the lost bone. I would suggest avoiding this option. Depending on how deep the permanent canines are impacted, and how long the roots of the primary canines are, you may be able to veneer the primary canines to make them appear like permanent canines. Consult with an aesthetic dentist to discuss if this could be an option in your case. 

Yes you can have the baby teeth and the unerupted canines removed and place implants.  Depending on the position of the unerupted teeth and the ability of the surgeon, you can lose a lot of bone around the area which would compromise ideal implant placement.  There are ways to erupt the canines with lingual braces you can't see.  There are other options.  It's hard to make a suggestion without seeing a 3D cone-beam scan.  This should be done before any decisions are made and any predictions are made.