To 'get a foothold on something' is a locked phrase, and there are many of these in English. Your first instinct to keep the original phrasing is correct. If you were to change it to 'help getting', then either you'd have to include the missing preposition 'in' so it becomes 'help in getting something' acting as a phrasal verb, or if not, then 'help' becomes a noun at the end of one clause and 'getting' becomes a noun (in gerund form) at the start of a dependent clause. Here's an example: I got some help getting the car. Let's parse this: [I got some help] [getting the car]. Your example, parsed: [Climbers can strap sharp nails on] [to help get a foothold on a slippery slope].
I would also recommend not ending the first clause with the preposition 'on' to avoid structural awkwardness, and change it to 'Climbers can strap on sharp nails', thereby keeping the preposition closer to the main verb.
Hope this helps!!
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