Fast glass (2.8 or better) and at least a "semi-pro" body capable of rendering high-ISO images relatively noise-free is the only way.
+1 to that!
I've spent several years learning and remedying the ins and outs of in-church photography without the use of flash. Fortunately, it's the church where I am member, and they've never had a problem when I (or anyone else)uses flash.
It all comes down to the exposure triangle. You will be 'pushing' your equipment and skills to the maximum. Obviously, one absolute requirement is 'fast glass', f2.8 and faster (smaller f stop numbers). But shooting that wide open results in narrower depth of field, which can be increased simply by moving further back. If you end up shooting 'wider' than you want in the picture, it's easy to crop out the excess in post processing...if you have 16mp or more to start with. Lower than that, you'll have to limit your cropping to keep 'enough' pixels to keep a good, clear image.
Depending on your camera, you'll need to be setting the ISO as fast as possible without too much noise in the picture. What 'too much' is depends on your own tastes. If you haven't already determined what your highest acceptable ISO speeds are, you definitely need to do so BEFORE the wedding.
Fast glass, fast ISO, what else? Fast shutter speeds, too! Although there are times I've shot with shutter speeds as slow as 1/10th, at those speeds, the non-blur keeper rate is less than 1 in 25!...or worse! Shooting at 1/30 improves the non-blur rate to about 1 in 15, or a bit better. At 1/60th, if the subject (bride and groom) are reasonably motionless, the no blur rate is about 1/5. Even at that speed with a 1 in 5 'success' rate, would you be willing to 'risk' the 'kiss the bride' shot? I didn't think so. But if ISO and aperture are already at your 'limits', you won't have a choice. If you can shoot at faster shutter speeds, then do so. But don't forget that the wider-open the lens, the narrower the depth of field! Ideally, shutter speeds of 1/125 or 1/250 will stop subject (and camera) motion blur. But unless you can comfortably shoot ISO 6400, those shutter speeds are quite unlikely.
And since you are taking pictures of moving subjects (even their breathing is movement), be sure to use the AI Servo auto-focus setting so the camera tracks their moving. Nikon has some other name for it. I used to think that one-shot auto-focus was workable, but it turned out to be responsible for a large percentage of my subject motion-blurred images. Switching to AI Servo made a major improvement in reducing subject blur.
Additonally, the non-blur issue is affected by camera shake at low shutter speeds. That's why image stabilization is required at those speeds..IS/VR/whatever. That will reduce camera shake issues. If you can, I strongly recommend a monopod with a swivel head. That will add even more camera stability, thereby reducing blurred shots. Monopod heads are designed to move in on plane of movement only. I prefer a ball head on mine, as I am often leaning against a wall or pillar for added stability, resulting in the camera and monopod angled upward as a result. The ball head makes correcting that very easy to do.
Lastly, depending on your post processing skills, you can under-expose slightly and correct it in post processing. I'm thinking about 1/2 a stop. You may lose some darker details, but in my mind, that's still better than losing the shot. And, if you have to, cranking the ISO up just one notch more (1/2 or 1/3 stop) will give more noise than desired, but, again, which is better, a slightly noisy picture or no picture at all? There's also some very well regarded noise reduction post processing programs available as well that 'can do wonders' with noise. I have no doubt the pros out there are cringing as they read this paragraph, but I'm an amateur as are you...so we can 'get away with it' and not hurt our business.
Bottom line, know your camera AND your skills as best as possible. You will be pushing BOTH to their limits!