For a lot of sports such as tennis, basketball etc., the verb play can be used. When it comes to other sports such as judo, powerlifting or even swimming using the verb play feels a little strange to me.
In this case, what do you think the most suitable word to use would be and is there a specific reason why the word play just doesn't seem to fit?
There are three verbs which can be used with sports: play, go and do.
According to https://www.ecenglish.com/learnenglish/lessons/play-go-do,
Play
Play is used with sports that have teams, rules and competitions:
Badminton, baseball, football, golf, rugby and tennis are some examples.
I have been playing tennis for over ten years.
When I was young we played football just outside our house in the street.
Go
Go is used with activities where the activity is in the -ing form.
To camp – go camping
We went camping by the lake last summer.
Other activities that take 'go' are: dancing, jogging, running, hiking, riding, swimming, cycling, climbing etc.
Do
For all other recreational activities we use do. Aerobics, athletics, gymnastics, judo, karate and yoga are some examples.
All young children should be encouraged to do gymnastics.
Sarah does yoga with some of her friends.
Also, please note that using go implies that it is neccessary to travel somewhere (or... well, literally to go somewhere) in order to start doing mentioned sport, but you would actually do sports ending on -ing if you're already at the gym or some facility (pool, climbing gym, etc). Please compare:
I would like to go powerlifting tomorrow.
I often do powerlifting at the California State University gym.
As a result, use do with judo. And the reason play doesn't fit is that it's used, again, with sports that have teams, rules and competitions (i.e. games - football is a game, volleyball is a game, hockey is a game, chess is also a game, although it usually involves only two players, and so on). Hope that helps!
P.S. As it was said in comments, you can use swim without anything, because it is a verb that can stand alone:
Rebecca swims fastest in our class.
I used to swim often when I was 12.
I swam five kilometers.
