It's never better to use an unspecified code if you have documentation that points towards more specificity. The ICD-10 guidelines state:
b. “Unspecified” codes
Codes titled “unspecified” are for use when the information in the medical record is insufficient to assign a more specific code.
Also, many payers are starting to push back on unspecified codes when more specific codes for laterality exist. If your documentation states that the arthralgia is bilateral, then you're correct that M26.623 is the appropriate code to use. You'd only use the unspecified code if your documentation didn't give the laterality.
Regarding your other question...
N35.01 is not a complete code - it requires a 6th digit. Additionally, the N35.01- category is for male patients. Since you said that it is from an obstetric injury, I'm inclined to think that you need a code from the N35.02 category, which is for female patients.
N35.021 is Urethral stricture due to childbirth
Here are examples of a few lookups in the Alphabetic Index that would map you to the N35.021 code. (This may not be a comprehensive list - these are just some of the pathways I found in the alphabetic index based on the keywords you gave)
Stricture
Urethra
postobstetric N35.021
Stricture
Urethra
Sequela (late effect) of
childbirth N35.021
Stricture
Urethra
post-traumatic
female
due to childbirth N35.021
Stricture
Urethra
due to
trauma - see Stricture, urethra, post-traumatic
Stricture
Urethra
late effect (sequelae) of injury - see Stricture, urethra, post-traumatic
Hope this helps!