"Packets" and "liners" may have been "clippers" but not "cutters." A "cutter" is either a single-masted sailboat, or else a lightly-armed vessel of any kind operated by a nation's nautical anti-smuggling service.

So a "Yankee cutter," in the song, can only be a vessel of the U.S. Coast Guard (which took that name in 1915)or its predecessor, the U.S. Revenue Cutter Service (formerly "Revnue Marine").

So the "cutter" part of the verse is a bloper. If it matters.

So pass that belayin'-pin pie! Can I have a scoop of vanilla on mine?