Beware.... 20" is an old system and believe it or not covers a while series of sizes.
This guide is a useful starting point
The better way is to look at the present rim / tyre and look for the ERTRO number. It will be in the format XX-YYY
In your case without the tyre, it will be stamped onto rim
The first number is the width of the tyre and can be altered within reason (a narrow racing tyre would be 25mm, a hybrid touring 37mm and a large mountain bike up to 50 mm
I would suggest that a 37 mm or similar would be fine for your needs, as it gives some softness to the ride
The second number (YYY) is the important one as this is the actual size of the wheel and so long as this matches the tyres will fit
20" tyres range from 406 to 451 mm in diameter, a massive 2 " in the diameter
Older wheels used the 451 and modern small wheels like folders and recumbents tend towards the 406
Some longstanding models changed as the 451 tyres became less available and more restricted in changing the wheels to 406 to give th wider availability and choice
Therefore depending on age your trike may have either
