Gotchas converting latin1_swedish_ci to utf8mb4_unicode_ci
I assume you will do this for each table?
ALTER TABLE tbl CONVERT TO CHARACTER SET utf8mb4;

One potential issue involves the maximum of 767 bytes per column in an INDEX.  If you currently have a VARHAR(255) latin1 field in an index, you will need to rethink it.


Decrease it to VARCHAR(191) if you are sure that 191 will suffice (into the future)
Use a 'prefix' index:  INDEX(foo(191)).  This is often not worth doing.
DROP the index.  (But not if you need the index; let's see the SELECT that needs it.)


Edit

For shrinking to VARCHAR(191), you could write a Stored Procedure to look in information_schema to discover all the VARCHARs, and create and execute SELECT MAX(CHAR_LENGTH(col)) ... to see if any are over 191 (or even dangerously close to 191).  You might be surprised to find a few with max=255, implying that you may already have truncated some text.

The other two options won't damage data, but could have performance problems.