Yes, some part-time programmes do not offer honours. It really depends on what kind of career you are looking at? If the job min requirements do not require honours then it does not really make a difference. Some government positions require honours. I suggest you do more research on the career you intend to pursue so you will make a more well-informed decision
yeah, some of them don't, though i wouldn't say most or all of them. some students are invited to do honours even though the honours track isn't explicitly mentioned on the programme brochures/website. you could try emailing the heads of programme to check since they would be in the best position to advise you (their contact details can be found on the website)
i agree that it really depends on what you plan to do in future but i feel it's not do or die. just pick something you're interested in and do well in it =)