This is an interesting question and since no one else has attempted an answer, let me try to provoke some discussion. The question specifically addresses less common uses of nickel since the most common use of nickel is to combine it with iron to form stainless steel (i.e., approximately 2/3 or more is used for stainless steel).
It is also used in other alloys or plating that account for another 20 percent or more. It is in this area that demand might change as a wide variety of metals can be used to form alloys or less commonly in plating.
Another source of a shift in the demand for nickel is in batteries (e.g., Nickel-metal-hydride or NiMH). Newer battery technology might replace these batteries because of the so-called "memory effect" of NiMH batteries. Although NiMH batteries still may be more cost effective per charge in some applications, many of us may prefer the Lithium-ion (Li-ion) batteries that seem to hold their charge longer. For example, I have multiple high-quality 18 volt drills. (Can a guy have too many drills?) I find myself using the Li-ion drill the most because its power does not fade; however, it just stops when discharged with little warning. Each has advantages, of course.
I strongly suspect that battery technology will continue to improve, especially in electric cars; however, it seems unlikely to me that the technology is moving toward nickel-intense batteries. Batteries probably account for around 2 percent of nickel, so only a large increase is likely to change the outlook for nickel overall.
Another issue with nickel is that a surprising number of people have allergy related issues with it. This is potentially an issue.
Perhaps the greatest change may have to do with alloys created in China. My experience with Chinese manufactured goods made of metal is mixed. For example, I used to think of metal brake rotors as a standardized good and although they typically contain little if any nickel, I suspect that the principle remains the same. I strongly suspect that those buying alloys will be more careful in their purchases as they recognize (or maybe just perceive) differences in quality.
Although the question by Erkan Yesel specifically addresses the non-stainless steel outlook for nickel, similar quality issues with stainless steel might change the overall outlook.
Since I have already veered outside the scope of the question to some extent, a couple of supply issues are worth noting. First is the relative abundance of nickel on earth and secondly as an export it seems to be exported from places like Ontario, Canada, Australia, Cuba , and Indonesia; that latter two may present some stable supply concerns, especially as Indonesia recently moved to ban or reduce exports in this area.
Considering all of these, I suspect some changes in demand; however, these changes do not seem to be dramatic changes. Short run changes in supply are another issue and they seem to be driving the price of nickel right now.
I trust others will improve my answer with corrections, better examples, or more information. Like most economist, I enjoy attempting to analyze things like this and look forward to the refinements others offer.