I don't recall which kit you have. Is it a vibrato bridge or hardtail? Either way, pickguard screws will not be suitable. TBH, I wouldn't use the kit screws for any bridge. They tend to be pretty poor quality and I've seen them twist off when turning them in.

Since it sounds like you need to buy screws anyway, get some quality ones from a guitar parts/luthier supplier. Whilst you may get appropriately sized screws from a hardware store, they likely will not be chrome or nickel finish or have the right shaped head.

A word of advice (even using good quality screws) is be sure to drill correctly sized pilot holes and use a tiny bit of wax on the screw threads (I prefer bee's wax*) and they'll glide right in and greatly reduce the chance of breaking off.
*You can use paraffin or candle wax or even a bar of soap, if you don't have bee's wax.

Here are some examples of typical bridge screws for vibrato and hardtail: (note screw sizes in links)

Vibrato bridge screws

Hardtail bridge screws