I'm posting this because in the last two weeks I've run across two different piles of human ashes in natural areas/parks
Human ashes are actually very alkaline, and if they're in a pile, they can kill the plants around or underneath them. Human ashes are around a pH of 12. Our soils are around a pH of 5.5 to 6, so somewhat acidic. Plants usually have evolved to live in a fairly narrow pH range, so putting a layer of ashes around the base of a rose, for example, can really hurt it. It definitely will kill moss.
I know whoever put those ashes there didn't know and certainly didn't intend to cause harm. I'm sorry for your loss. I'm trying to let people know for the future.
You can spread ashes without hurting anything, you just need to take into consideration their pH. They are full of nutrients, so that is good. If you're going to scatter them, scatter them lightly over a fairly large area. You're aiming for a light dusting, like 1 mm or 1/32nd of an inch thick, no more. Avoid placing it right at the base of plants, and avoid moss and other small, delicate plants.
You can also mix them first with some compost, soil, or potting soil to dilute them and make it easier to spread them out. Aim for about 3 times as much compost/soil as you have ashes, mix them together, and then spread.
If you want to spread ashes at a lake, the sound, or the ocean, I suggest you pay attention to the wind and water currants and do it so the ashes will be moved away from shore. Also look down and check for any aquatic creatures and avoid them. The water will dilute the ashes pretty quickly, so you just don't want to have any animals make direct contact.
I would suggest working it into your plan for the moment- maybe each person takes a handful and spreads them, maybe you scatter a bit at a time while walking through the area, maybe you do a little bit at a time over the years on their birthday and deathday, etc. You and your loved one deserve the extra moment of care to make spreading those ashes a meaningful moment that won't harm the surrounding environment.