I want to say "using a grapple hook" as a verb. In context it would be like "sprinting, jumping, grapple hooking"—but that doesn't sound right. Is it correct? If not, is there a way to say it as a verb?
In a "composite verb" to mean hooking with a grapple hook, the verb component is to hook [with something], so the present participle must be grapple-hooking.
I can't actually find a written instance of OP's exact form, but here's
...which illustrates the general principle (a verb is a verb is a verb). It's really a matter of style whether you include the hyphen or not, but I think most people would prefer it to be there.