No, Not Kettlebells!

Kettlebells are not a good training tool for HEMA. Let's start there.
They are a perfectly good tool for burning calories and meeting generalized fitness goals, but not for meeting the needs of a fighter.

I do want to get out of the way one point: I'm not opposed to kettlebells. Their are two minor quibbles I have with them, neither of which is significant enough that I'd tell somebody, "don't use them". But I sure can't recommend them.

1) They cost more. For the same amount of money you can buy a larger amount of weight in dumbbells and the DBs will be adjustable at that cost, but the KBs aren't. So, I would tell people not to buy kettlebells.

2) The handles don't rotate. Many KB exercises involve the bell rotating in your hand. This will cause, and then rip open, callouses more than other weight lifting tools. So that's not good. The problem isn't awful, it's  annoying, and but it can get in the way of training on those days when your hands are messed up. And that's a problem for people who train with weapons.

The best kind of strength training for HEMA is something that I've covered before. The important aspect is that good strength training for fighters is going to have one of three aspects: max force, max power or max velocity. Kettlebells are not heavy enough to elicit either maximum force or maximum power from the muscles. And they are too heavy for you to be able to generate max velocity.

Working in and around these maximums - force, power or velocity - produces the greatest benefit for the amount of time spent working out.

Max Force - Exercises which require high force production will recruit the largest motor units and the greatest proportion of your muscle fibers. This is the result of the Size Principle, and what it means is that low load exercises will simply not ever trigger the use of your biggest motor units. When you use your biggest motor units they get bigger, stronger, faster and are more easily turned on by other actions. As you train at high loads you will use your big muscles more in your fighting, so you will produce more force and power.

Max Power - Maximum power is generated in between 30% and 70% of maximum force. Different studies have found different ranges of values that elicit max power and it varies with the particular exercise and muscle groups being used. The highest power output exercises are the Olympic lifts: Clean & Jerk and Snatch. At their peak these exercise can be measured in Horsepower, with elite athletes producing over 7 horsepower. Seven horses! Kettlebells can't even get close to that. Kettlebells just aren't heavy enough. Even a small person, at 100 lbs. would need KBs around 50-60 pounds to generate max power and that person could easily train until they need over 100 pounds to elicit max power.

And their are lot's of other good reasons to do Olympic lifts, too.

Power is relevant because it is a measure of how quickly force is produced. The same amount of force in a shorter period of time is higher power output. As strikes happen faster than the muscles ability to reach maximum force the faster that force is produced the more effective the attack. (And max force still matters because in a given amount of time your muscle will produce a percentage of max force).

Max Velocity - Velocity of action drops off quickly as weight goes up. Enough so that above double-weight you get a steep drop-off in the carry-over from training to fighting. Therefore training velocity with tools above 4-6 pounds (for longsword) doesn't work well. This is why kettlebells don't do a good job of working velocity. Furthermore, velocity training is more movement pattern specific than the other two categories, so common KB exercises like swings just aren't relevant to fighting.

The better training tool for combining strength with velocity is an overweight waster (and heck, it's even historical).
You can also do a variety of plyometric medicine ball exercises for the upper body and trunk.  These are best with a light med ball (again 4-6 lbs. for longsword) that bounces well.

Conditioning is not Strength Training
This is a key caveat to everything I've said so far, which has been about strength training. For conditioning purposes kettlebells can be just as good as other approaches but not with typical KB programs. Most KB programs are geared towards increasing the amount of time or number of repetitions in a fixed period of time or a fixed number of repetitions in decreasing time. These kinds of programs are usually lacking in that they do not match the energy demands of a fight particularly closely.

A typical fight involves long periods of low intensity, while the fighters jockey for position and wait for a good tempo to attack. Then there is a brief period of maximum intensity. Each exchange usually lasts no more than a few seconds (if there's no grappling). Exchanges not infrequently last less than one second.

If your kettlebell program looks like that then great. But it probably doesn't. I've talked about conditioning before. And I'll go into more detail in the future.