Implications for the candidate if a contacted external evaluator declines
Chairs / deans / provosts will tell you that declining will have no effect. This is the official and morally as well as legally correct answer.
However, I've had the great pleasure (not) of serving on a committee (at a private, elite R1) where the promotion review chair did not like the candidate and raised the issue that there were a certain percentage of declines to strengthen their tenuous case against the scholar ("no one likes/respects this scholar thus they are declining to serve as reviewers).
This was counter to policy and in my mind immoral and possibly illegal depending on the circumstances.
If you do decline, please include a phrase that you are declining due to personal / workload reasons and that the committee must absolutely not use your declination to in anyway prejudice the candidate's case.
Now as to your subsidiary question as to whether you should feel obliged to write, this is more of a moral question. As a tenured full professor, I do feel an obligation to my discipline to do these reviews.
However, I will only do a review if I can do it well. If a candidate's work is out of my field of expertise or if my workload prevents me from doing a good job, I won't write. My first obligation is, after all, to my research agenda and my students.
Furthermore, there have been cases where I know too much about a candidate to write an objective review. In those cases, I ask to be relieved due to a conflict of interest.
There are varying opinions on whether one should write negative letters and this should really be a separate question. My own philosophy is that my letter is a third-person's neutral observation of the strength of the candidate's application for tenure. I thus write about the strengths that I see for this case, but whether the strengths are sufficient for tenure is ultimately a decision that should be made by the tenuring committees.
As a preface to this answer, I've only been involved in the promotion process at relatively elite private R1's. Things might be different at more teaching oriented schools.
With that said, I disagree with RoboKaren's answer. At the places where I've been involved, the promotion dossier includes a list of all people who were asked to to write letters. For those that declined, the reason for their declination is also listed. University administrators have been very explicit that a low acceptance rate is bad for the case. That's not to say that any single declination is going to have much of an effect, but a large number will. Though I've never sat on a university wide promotion committee and thus have only seen mathematics dossiers, I've been told that the acceptance rate in math is higher than in other subjects, so this mostly hurts non-mathematicians.
As far as your scruples about writing a letter, please do not write a negative one unless you have a very strong opinion that the candidate should not be promoted. A single negative letter can torpedo a case. It is better to decline.
For the letters I've written for people at teaching institutions that have limited time for research, my strategy is to make comparisons to people I know at similar kinds of institutions (perhaps at places that are slightly better and thus are aspirational peers rather than actual ones). There is no reason to compare them to people at R1's. Sometimes the university will try to box you in on that (eg they will ask you point-blank "Would you support tenuring them at your institution?"). I always just side-step such requests (eg with a statement that if I were at their institution, I would enthusiastically vote to promote them).
A final comment. You say that one problem for you is that you might have to investigate things like whether or not a paper has been published. I see no reason to do that. I just take the cv/publication list/research statement at face value unless I have a really good reason to not do so. You shouldn't make writing these letters in a big ordeal for you. I usually give myself a single afternoon (say 4-5 hours at most) to write the letter and try to keep it at that.