It could be better to use PGP, which has been designed to encrypt files.
Only OpenSSL v1.1 latest versions contain a command line switch to choose the number of iterations (the work factor) to configure the password hash when using password based encryption (PBE). This is something that is required, otherwise the password must be of about the same strength as your original password. That would of course not help you any further.
As you require just normal confidentiality you could just use AES-CTR mode for PBE. Then there is just 16 bytes of overhead for the salt and header (you could remove the first 8 bytes of magic and replace it back afterwards as optimization). So then the ciphertext would be only 8 bytes more than the password. Base 64 - you can forgo the base 64 padding characters - will just expand this by one third.
However, the password consists solely of lowercase characters. So each character only needs to take 5 bits (2^5 = 32 which is greater than the 26 values required). So that way you can save 3 bits per character.
So the minimum size of the maximum value would then be 24 * 5 / 8 = 15, 15 + 8 = 23 bytes, expanded to (24 / 3) * 4 = 32 base 64 characters.
But don't forget to write down or remember the iteration count and - of course - the algorithm itself.
It might be easier to use e.g. an IronKey to store your passwords on a USB stick (or two), which would cost you about 50 Euro per piece. Remember that flash may not last forever though, it can leak state over time.