preferably, this should be done on days other than a friday - so that the jumu'ah schedule is not busy. [dawat e islami edition vol.16 p.582 / takhrij was not given] the hadith mentioned is from tabarani, as mentioned by suyuti in al jamiy al-saghir. he noted that it is weak. there is no linking of these actions. it is just practice that people anyway shower for jumu'ah and do the actions prior. if it does not interfere in your jumu'ah schedule. doing so is also ok - as per the hadith above. in fact, in arab countries, it is difficult for most of them to rush - because eid prayer is done immediately after the makruh time. on-the-dot 20 minutes after sunrise/shuruq. only those who go to the musalla/eidgah can think of it prior to prayer. Allah ta'ala knows best.
that is because, you can do it comfortably and focus on azkar prior to jumu'ah and prepare for jumu'ah. bahar shariat: vol.4 /p.776 (DwI ed) if one wants to get a haircut or trim [beard] and nails on a friday, then it is preferred to do it after prayer.
i've seen people say that on Fridays nails should be cut after Salatul Juma, as that way the nails get a chance to be included in the salah. is there a direct hadith basis for this? fiqh rulings in our Hanafi mazhab? other mazhabs rulings? does this also apply to shaving body hair like underarms etc.? shouldn't all such actions be completed prior to the Sunnah shower for Jumah? --- does the same also apply to Eid al Fitr? --- for Eid ul Adha it is well known the person doing adahi should (highly recommended not wajib) stay without shaving body hair, trimming facial hair, or clipping nails, just like muhrim's, till he slaughters.