The ridge route is roughly parallel the valley route, and covers a similar distance. There are several pros and cons in comparison with the valley route. The ridge route does involve climbing some gentle peaks on a long ridgeline approach to get to the base of Makushin itself. This might add up to around 1500 more vertical feet or so to your total climb in comparison with the valley route. The valley route involves a lot of bogs and bushwhacking through vegetation of varying heights and thicknesses, as well as insidious swarms of black flies in summer. So it becomes a matter of picking one's poison.
Similar to the transportation required for the valley route, the ridge route begins across the bay from the town of Unalaska. But rather than starting in Broad Bay where the Makushin River drains, you will continue a little farther to the northeast just past the next ridge. There is a large waterfall that marks the small cove, and the cobbly beach there drops off well enough to make landing a skiff easy enough.
Once on the beach, you follow a ridge on your left as you look inland. It's not particularly steep, but does ascend fairly quickly to around 1500 feet before leveling out. Once on the ridge, Makushin itself will come into view in clear weather, and will remain in view to the west for much of the hike. There are some ups and downs, with a particularly low saddle where the drainage on the right feeds into Reis Bay, and there will be a lovely little lake on the broad saddle. After that the route will begin gaining more elevation. You can side hill some of the peaks if you wish to avoid gaining unnecessary elevation, but the last set of peaks before dropping onto the plateau at the base of Makushin will require you to ascend over 2000 feet at the minimum to get around an otherwise impassable gully that drops sharply to the Makushin Valley on the left. After that last climb, you will descend onto the broad plateau that separates Driftwood Bay and the Makushin Valley. This is where the valley approach meets up with the ridge route.
There's nothing technical as far as climbing on this route. In Winter or Spring, it will be snowy, but with very minimal if any avalanche danger as the ridge is broad with generally gentle slopes. You'll want crampons or at least micro spikes, and an ice axe might be needed. A GPS wouldn't be a bad idea to deal with cloud cover which can obscure whole sections of the route at times. If nothing else, a map and compass and good navigation skills should get you through anything but the absolute worst whiteout as long as you know what you are doing.
Gear required for the volcano itself will depend on conditions, but being ready for glacier travel is the most important thing. While the crevasse danger is low to almost non-existent on the main route, there are crevasses that may be wide enough to swallow a person, especially if you get off the main line.