Sacrifice does not necessarily meaning killing. Check:
Heb. 13:15 Through Jesus, therefore, let us continually offer to God a sacrifice of praisethe fruit of lips that openly profess his name.
Ps. 50:14 Sacrifice thank offerings to God, fulfill your vows to the Most High
Numbers 8:915 Aaron is to present the Levites before the LORD as a wave offering from the Israelites, so that they may be ready to do the work of the LORD.
Besides, the sacrifice of the mass is the participation in the ONE sacrifice that was Christ's sacrifice.
You do seem to understand a SIN OFFERING
shalom b'SHEM Yah'shua HaMashiach
as opposed to a thanksgiving or wave offering.