Interestingly, there's more than one mechanism for making spiderweb sticky. The method that most people are aware of is by adding tiny droplets of adhesive to some of the threads. There's a separate group of spiders called cribellate spiders that produce very fine silks that can have a "fuzzy" texture that prey can easily become entangled in. Alternativesly, the oils and waxes on the prey's skin or carapace can stick to the fuzz, adhering it in place without the need for the spider to produce glues. Cribellate orb weavers exist producing complex web designs.
There are a number of approaches that cribellate spiders take to acquiring prey that might be relevant to your interests, though. The spider in the image above, Progradungula otwayensis, is an ambush predator. It waits for foolish prey to come nearby, then scoops them up into the little snare it has assembled and administers a good toxic fanging whilst the prey is entangled. Similarly, Deinopsis species, called "net-casting spiders", amongst other things, spin small webs which they detatch and hold with their legs, and grab passing prey with those. Triangle web spiders build a partial section of a non-sticky orb web which they hold under tension from one corner. When prey hits the web they let go, and the silk springs back thoroughly entangling the prey without the need for immediate further wrapping or adhesives.
My other favourites are trapdoor spiders, a number of different species who build a burrow with a camouflaged "lid" which they lurk underneath. Radiating from the entrance to the burrow are a number of silk lines which the spider feels the ends of. When prey walks past close enough to the entrance to the burrow they disturb the silk, alterting the spider to their presence and their direction. The spider then pops the trapdoor open and pounces. Relevant video, not for arachnophobes. Funnel-web, tube-web or radial-web spiders use similar tricks, without the camouflage lid.
Tangle webs or mesh webs are another cribellate web form with a flat sheet below a seemingly random arrangement of strong, fine silk lines. Passing flying insects hit the crosslines and fall onto the sheet underneath where the builder can finish them off at will.
As you can see, the real world provides a wealth of techniques for you to
steal be inspired by, but I'm sure there are plenty more that could be conjured up... webs used as a lure, animated by the spider pulling on threads, to tempt in would-be predators. Underwater nets, perhaps like the classic conical fish trap design, that swimming prey can enter but find difficult to leave (perhaps spun by an equivalent to the diving bell spider). Might think of more later...