Would a solution be as simple as getting a replacement pair of woofers and hooking them up?
Yes - provided you find the correct replacement woofer from Dynaudio. It is very easy to replace woofers in most speakers. I am not familiar with Totem One's but I expect is is a simple matter.
However, Dynaudio stopped selling drivers to DIY and hobbyists around 10 years ago - so good luck! Your best bet is probably Totem but it will likely be fairly costly as the reality is that it is expensive for boutiques to support a 10 year old product when they OEM all the critical bits in their designs. (Remember Dynaudio makes money on parts, Totem cannot sell you a replacement part at a loss - so they make money, and finally no dealer in their right mind would take some risk to help you for no profit. All this is necessary otherwise these people go out of business)
You may be able to find someone who can repair/rebuild the voice coils but I doubt it is worth it unless they happen to be local.
In the end it may be simpler to look for another used old pair on line. My recommendation to those making serious investments in high quality 10 year old used speakers is to check whether the company still supplies replacement parts...many do but most do NOT.