UPDATE a column in every row with a random unique number

I have a small table of about 20k rows. In that table there is a column named random_uid (INT NOT NULL). I would like to update all 20k rows with a random unique number.

Since my table is small I dont think I need to use a string or a UUID so I went with

SELECT FLOOR(RAND() * 100000000) AS random_num
FROM table1 
WHERE "random_num" NOT IN (SELECT random_uid FROM table1)
LIMIT 1;

My problem is that I cant update and select from the same table, so I was having trouble creating the UPDATE query.