The following is a statement from William Perkins on the Efficacy of the Sacraments. Notice that Perkins does not allow for us to speak in different categories with regard to how we understand the sacraments as signs and seals. Keep in mind, Perkins was the father of Elizabethan Puritanism, and every delegate to the Westminster Assmebly would have been well schooled in Perkins when drafting WCF Q&A 161.
On the Efficacy of the Sacraments:
The difference between us [Rome] stands in sundry points. First of all, the best learned among them teach, that Sacraments are physical instruments, that is, true and proper instrumental causes, having force and efficacy in them to produce and give grace...Now we for our parts[Protestants] hold that Sacraments are not physical, but mere voluntary instruments. Voluntary, because it is the will and appointment of God to use them as certain outward means of grace. Instruments, because when we use them aright according to the institution, God then anwerably confers grace from himself. In this respect only take we them for instruments and no otherwise...We hold the contrary: namely, that no action in the dispensation of the sacrament conferreth grace as it is a work done, that is, by the efficacy and force of the very sacramental action itself, though ordained by God: but for two other ways. First, by the signification thereof. For God testifies unto us his will and good pleasure partly by the word of promise, and partly by the Sacrament: the signs representing to the eyes that which the Word does to the ears: being also types and certain images of the very same things that are promised in the Word, and no other.