Is a lateral canthoplasty to lower the outer corner and extend the eye safe to do so?

Yes. Under eye rejuvenation is best corrected by surgery but there are some nonsurgical options as well. The procedure is safe and completed in minimal time. Eyelid Rejuvenation is one of the first cosmetic surgeries people usually get. While the average age might be 30 to 50's, some patients get this done in their 20's. It really depends on your unique anatomy as well as what exactly is bothering you.
The recovery & downtime is very minimal. There are usually no drains, most people can go out the same day, you can shower the next day and most patients take no pain medicine. There are never any guarantees of course with any procedure whether it is surgical or nonsurgical in nature.

Surgery is not for everyone. In today's day and age, there are many nonsurgical options to consider although surgery usually gets the most improvement specifically of the malar or lower eye fat bags.
I would recommend that you see a board-certified plastic surgeon in your area that is a member of both ASPS & ASAPS and performs a lot of mini facelifts and eyelid lifts but also offers all the nonsurgical options such as injectables and laser treatments. Go over your concerns with them and make sure above all, you walk out of there with several options and an idea of the pros and cons to each of them as well as realistic expectations.
I hope this helps and wish you all the best in your surgery and event. If it does, please take a moment to up vote this answer on the “respond” button on the top right. 

Hi and welcome to our forum!The lateral canthoplasty involves detaching the lateral canthal ligament from its insertion at the lateral orbital rim and reattaching the ligament higher or lower at the lateral orbital rim to change the slant of the lid. It is a safe procedure and is usually performed on an outpatient basis.Visit a board certified plastic surgeon for evaluation and discussion.Best wishes...