We do not usually recommend pushing off a hefsek taharah. When both spouses agree, however, it is permissible to push off immersion after the clean days are complete.
It would be most preferable to immerse on time. We suggest that you and your husband discuss different possible ways in which you might be able to manage a Friday night immersion with a minimal amount of embarrassment. Sometimes a little creative thinking can go a long way. Being open about your immersion with one family member or other key individual in a position to help can also make a difference and would be permissible for this purpose.
Please write back with any further questions.