If it's the @supports at the end of your css file that's causing the problem I'd just use the font-variant stuff without checking. I don't know if anything goes wrong if the font doesn't support them. For example, here's what I have in my template.epub file's css for headers (this isn't everything; spacing stuff taken out).
Code:
-ms-hyphens: none;
-moz-hyphens: none;
-webkit-hyphens: none;
-epub-hyphens: none;
adobe-hyphenate: none;
break-inside: avoid;
break-after: avoid;
font-feature-settings: "kern", "liga", "clig", "lnum", "pnum";
font-variant: common-ligatures lining-nums proportional-nums;
hyphens: none;
page-break-after: avoid;
page-break-inside: avoid;
For reasons I no longer remember (I probably just copied this from somewhere without trying to understand it) my css for body has slightly different stuff; oldstyle-nums instead of lining-nums.
Code:
font-feature-settings: "kern", "liga", "clig", "onum", "pnum";
font-kerning: normal;
font-variant: common-ligatures oldstyle-nums proportional-nums;
text-rendering: optimizeLegibility;