Even if you could sign, is there another email client out there that could decrypt them? You might find, as with Enigmail/GPG, that you're limited to a very select circle of correspondents.

It does seem odd given the apparent benefits of ECC over other encryption systems that it doesn't seem to have gained any traction in email.

I am testing one PKCS#11 library and I need an email client (that will use this PKCS#11 library) capable of signing with ECDSA keys. So I don't care if anybody will be able to decrypt it. Just need to test my P11 lib with some application.

GnuPG claims to support Elliptic curve cryptography from version 2.1.15. So I suggest you look as the options provided in the PGP add-on for Thunderbird.

https://addons.mozilla.org/en-US/thunderbird/addon/enigmail/?src=hp-dl-featured