If you are happy summing several items (or taking the mean or otherwise using the arbitrary codes to create a composite score), you already assumed more than merely ordinal measurement so you might as well go for the t-test.
On the other hand, if you want to be absolutely strict in treating your data as ordinal, the Wilcoxon signed-rank test is not particularly helpful because it is based on a ranking of the differences between pre-test and post-test scores, which means assuming than $2 - 1$ is the same as $4 - 3$ and therefore than the codes you assigned to each response have some meaning beyond their order (see Is ordinal or interval data required for the Wilcoxon signed rank test?).
In fact, the Wilcoxon signed-rank test is most useful with measures that are continuous and interval-level but have poorly behaving distributions (skew, mixtures of normal distributions, etc.) In that case, it can have much better power than the t-test. So you might want to consider using it with scales' scores (composite of several items), not as a way to avoid assuming that your data are measured on an interval scale but to increase power.
If you are looking for a simple alternative, item-by-item sign tests would avoid any such assumption. However, with a relatively small sample, many items and very few categories, ties are going to be a problem, multiple testing issues, power and interpretation too.
All of these approaches (and some others) can be defensible but the popular notion that interval means t-test and ordinal means “non-parametric” is not a good way to guide analysis.