Jujitsu was born as a blade science. Some might think that's a provocative statement, but as you study the history of Japanese martial sciences you see it's true. Various forms of what eventually became collectively known as Jujitsu were developed and practiced by different clans, and different classes of society. It's common knowledge that the Samurai developed ways to deal with armed attackers with or without use of their own weapons, but other groups developed their own martial tactics; families and villagers protecting their property, criminals, monks, and various individuals who were not Samurai but never-the-less made a living by the strength of their fighting abilities all contributed to the Japanese martial legacy.
Each of these groups or individuals relied on some form of weapon or another as "force multipliers". You'd be a fool not to use whatever was available to increase your odds in life or death situations, no matter your station in life. For the wealthy, or paid warriors, the sword was the primary weapon. However various knives or other bladed tools were common to farmers, fishermen, blacksmiths, etc.
If you were smart enough or desperate enough to realize that a weapon could be utilized to increase your odds of defeating an opponent, it's likely you'd also realize what would happen if that weapon broke or just wasn't immediately available. Professional warriors, criminals, and victimized people are very practical by necessity. Otherwise they wouldn't be around long enough to pass on their lessons to the next generation.
So, we're discussing sciences of offense and defense developed by practical people; not arts and not sports. As these sciences were passed down and blended, they became more effective, just as we see martial sciences progress in our own lifetimes. Practitioners honed their personal movement, looking for the most efficient tactics. They realized that practicing one set of movements with a weapon, and a completely different set of movements without a weapon wasn't efficient. Thus, the tactics and movements they practiced consistently had to work whether you had a weapon in hand or not.
Obviously your targeting or distance may change according to whether you're armed or unarmed, but the principles of the movement will be the same. The principle of "Ju", or blending, was one of the primary components of Japanese strategies and tactics. Combined with other common offensive or defensive principles such as entering, leverage, etc, these became the basis of their armed and unarmed combat sciences.
So, the throws, sweeps, reaps, joint destructions, chokes, and targeted strikes, and all the combinations thereof which have become the "lists" of present day Jujitsu systems such as Danzan Ryu, Yoshinkan, Shoshin Ryu, and the Goju-Shorei Jujitsu System, were all designed to work with a blade, or unarmed. Again, you may have to change the range or target based on the length or presence of a weapon, but the principles of the movement should be consistent.
As you go through your daily practice of these "list" techniques, and all their variations, you should analyze how you would perform the technique with a knife in your hand. Would you be holding the blade in a forward grip, or reverse grip? Would your target change, or your angle to the target? While you're at it, change the tool to an impact weapon and see how you would approach the technique then. When you practice like this you'll deepen your understanding of the movement, and you'll be practicing the science the way it was developed and crafted to be utilized from the beginning.