Snap-dog--OED

Here is the listing for "snap" which includes under the examples "snap-dog." Dates are listed for usage as 1877 and 1891. However there are many earlier works that I have posted previously with references to "snap-dog."

1. a. With ns. (also forming derivatives), as snap action used attrib., as snap action gun (see quot. 1884); also to designate switches and relays that make and break contact rapidly, independently of the speed of the actuating mechanism; so snap-actioned ppl. a.; snap-apple (see quot. 1823); snap-bag, = SNAPSACK; snap-bean U.S. (see SNAP n. 18); snap-beetle, a click-beetle (cf. CLICK n.1 4); snap-block Naut. (see quot. 1884); snap-brim, used attrib. to designate a type of hat for men with a brim which may be arranged in different ways; also absol.; hence snap-brimmed a.; snap-bug, = snap-beetle; snap-cap (see quot. 1876); snap-dog, local, a lurcher; snap-dyke Sc. (see quots.); snap-fig, = BECCAFICO; snap-flask (see quot. 1875); snap gauge Mech., a form of caliper gauge that can be used to check that a component is neither too large nor too small within stated tolerances; snap-jack, dial. the stitchwort; snap-plough, local (see quots.); snap-rod (see quot.); snap-sound Path., a snapping sound heard in auscultation; snap-thought attrib., used for noting ideas as they occur; snap-tree, -weed (see quots.); snap-willow, local, the brittle or crack willow, Salix fragilis; snapwood (see quot.).
Other examples of this type occur in recent use, esp. dial. or U.S. Similar formations are also employed in Dutch and German.

1877 N.W. Linc. Gloss. 230 *Snap-dog, a half-bred greyhound. 1891 Pall Mall G. 23 Dec. 6/3 Rabbit Coursing Sweep~stakes for so many ‘snap-dogs’.