I've added a new toolbar set in config.js file:
config.toolbar_LinkOnly =
[
['InsertLink', 'Unlink', '-']
];
Then I went to Article page type, chose a field with Long Text datatype, this datatype has Rich text editor in form control property. And then I filled Toolbar set property with my toolbar set name
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After that if I try to create an article, I'll see link buttons only for the field.
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Be aware that your browser can save config.js file in cache, so you need to clear it after changes in the file.