TL;DR You may often replace 可以不用 with 可以不需要 without changing the nuance, but not in this particular sentence because "用" describes the action of "use", which would be lost if the word is replaced.
The actual difference here is the addition of 可以 before 不用/不需要. Because 不用, 不需要 are synonyms. The addition of 可以 brings up a suggestion, another option to the listener.
The following are definitions provided by the Taiwanese Ministry of Education.
不需要 is listed as a definition for 不用.
However, in your particular example, 用 also provides the sense of "use" in the clause, which may be lacking if "用" is directly replaced by "需要".
In here, "可以不用" takes on its primal meaning: "don't have to use" (more literally: is allowed to not using) but "可以不需要" would just mean "don't need" (more lit.: is allowed to not needing). So in the end, you may have changed "You don't have to always use a step counter or sports band" into "You don't always need a step counter or sports band".
So we would need to reinsert "用" somewhere else, like: 不需要使用/不需要用 (no need to use), where 用/使用 would be grammatically analyzed as being appended to the object to form a so-called "verb phrase", or an object which is just another predicate.
However, using the common phrase "不用" elsewhere, without the action of "use" would be synonymous to "不需要".
So here, I will continue to analyze the connotation of adding "可以-".
I believe the difference completely lies in the intention of the speaker. The effects of the sentences are exactly the same, where the speaker suggests doing something without the object.
可以不用/需要 - may do without. The speaker suggests leaving out the object, but it would have been fine otherwise.
不用/需要 - no need. The speaker suggests leaving out the object. Adding it back anyway might not be appropriate. In my personal opinion as a native speaker, this may a more polite way of saying "should not".
I have the following examples with their situations.
- 可以不用/需要付款. Connotation: You can choose not to pay. This might be some freeware distributed online, but the author could do with donations.
- 不用/需要付款. Connotation: You should not pay. This is a free service provided by someone and they do not accept payments for their volunteering work.
I do have something relating to grammar that I do not agree with @TangHo. They suggested these phrases may be paired with "+ verb" or "+ noun". However, I believe in linguistics analysis, "可以不用" and "不需要" are predicators/verbs. So adding another separate verb afterwards may not be appropriate.
The same goes in English, there can only be one predicator in a clause. As such, the sentence segment that comes after should be the object/complement. So a separate verb cannot come after "可以不用" or "不需要".
In English, the action-showing word placed after the finite verb would be called a gerund, which is analyzed as a noun, acting as the object. In general, this is called linguistically, Conversion or in Chinese, 轉類. In Chinese, part-of-speech conversions may be invisible, but in English, the spelling often changes.
I've given examples of appending "objects" above. Here are examples using "complements": "There is no need to be that quick."
- 可以不用/需要很快. Connotation: The speaker may prefer the action done quickly, but they are not in a rush.
- 不用/需要很快. Connotation: The speaker advises to do the action slower. There may be adverse effects when done quicker.