So Shadowsheath can be used on any weapon with ENC 2 or lower. If you were to use a Stripped attachment in order to lower the ENC of a Blaster Carbine (normally ENC 3) to ENC 2 or lower, can you apply Shadowsheath to it? This would assume that if you were to ever remove the Stripped attachment, you would no longer meet the requirements for Shadowsheath.

I read through the rules for attachments in the core rulebook (AoR version I have on hand), but it doesn't say anything about base stats versus modified stats being used to meet requirements.

I would say yes. Stripped down costs hard points, and this gives a very reasonable justification for doing so (beyond just being able to carry more).

I'd apply the common sense rule here. If it makes sense then sure, but if your stripped down weapon is still four feet long, just much lighter, then a shadowsheath isn't really a viable option.