With zero propulsion from the ship; you need a thrower and a catcher.
You might be able to use a powered magnetic rail gun (or coil gun) as both a thrower and catcher. They can fire projectiles 5000 mph in just 30 feet; in space you can make them as long as necessary to get up to speed in a survivable acceleration; even hundreds of miles long if that is what it takes. A pittance in space. And (like the coil gun) the rail sections do not have to be continuous; You can have manageably sized stages of acceleration, say a quarter mile each. Even thousands of them. Of course, I'd presume you have unlimited solar power to provide the transfer; you can locate as close to the sun as is safe and comfortable for power. Or you can use some sort of fusion engines to power the stages.
You can probably accelerate at 1G for as long as it takes to reach your desired speed.
The rail gun, with clockwise and counterclockwise magnetic fields, exerts a propulsive power on a projectile in single direction. So the same kind of gun can be used for deceleration as a catcher, it is just that coming in the opposite end, a propulsive power going "out" provides deceleration power for a projectile coming "in", i.e. traveling through the gun in the opposite direction. You don't even need to reverse polarity.
We might have a power problem far from the Sun, I'm not sure if recovering the momentum on deceleration can capture the power; but I'll presume not. So fusion engines at the destination might provide said deceleration power.
It would also occur at a safe 1G, in the same length of space. Of course power can vary at either end, depending on the mass of the ship, to reach a consistent final speed. Even if that is just turning on/off some number of stages in the rail guns.
Your only real problem is running into stuff, or missing the catcher for some reason; but otherwise there should be no drag in space.
In extant big railguns typical projectiles are about 6 pounds and accelerate to 5000 mph in 30 feet. I don't have the math at hand, but multiply both the mass of the ship by tens of thousands, and the length of the railgun by a hundred thousand (57 miles), and I think something in there would work. Recall that your ship is pretty much 100% life support for several weeks on end, no engines, etc.
Although there is zero on-ship propulsion, the ship might want navigational power, thrusters and such for docking with space stations, landing on a planet, etc.
And of course the destination "receiver" rail gun needs to be built in the first place! Builder ships might accelerate out by a railgun, but with no receiver would likely require fuel to slow down to their destination. But again, fusion engines.
You could even call it a "railroad", and like that, tracks must be build to a new destination, but the materials to do that can be carried as far as possible on the existing railroad.
And this is much like a railroad; accelerate to high speed, slow down to zero, and transfer to other rails to change directions.