Ss.........really long
ok, I am coming at this question from the standpoint of a dog groomer for almost 20 years.
There are no "hypoallergenic" breeds, I really don't care what anyone says. All dogs have saliva (and may lick, putting the saliva on the hair, and then scratch which spreads it), all dogs have dander (some more than others, a lot of times as a result of diet), and all dogs shed (just a matter of do they shed it off, and all over everything...like boxers, labs, beagles, etc. or do they hold it, and get matted.....like poodles, bedlingtons, soft coated wheatens, etc.)
As far as your list goes, you are looking for something smaller than a boxer. I understand that, although I live in a 16x65 mobile home and have had my boxer and her sister in my house.....both @ 50 lb and have had no problem with them playing......they play with how much room they have. Sure, they LOVE to have more room to play, but they wear each other out in the room they have. So, back to the list......
American Hairless Terrier--never heard of, have no opinion
Basenj --makes horrible howling noise, double coat, major shedding at least 2x/yr
Bedlington Terrier--lots of grooming care (brushing, trimming), don't know much else
Bergamasco--never heard of, have no opinion
Bichon Frise--lots of grooming care (brushing, trimming), can be snippy and barky
Bichon/Yorkie--mixed breed....never know what you are gonna end up with
Bolognese--not familiar with, have heard of
Border Terrier--possibly good choice, some grooming, wire-haired (fair amount of grooming)
Bouvier des Flandres--larger than a boxer
Cairn Terrier--possible good choice, some grooming, terrier attitude
Cavachon--not familiar with, no opinion
Chacy Ranior--never heard of, no opinion
Chinese Crested (hairless)--too small, too fragile
Cockapoo--mixed breed, never know what you are gonna end up with
Coton De Tulear--small, tons of brushing needed to keep from getting matted
Doodleman Pinscher--never heard of, no opinion
Giant Schnauzer--bigger than a boxer.....much bigger, but very, very cool dogs
Hairless Khala--never heard of, no opinion
Havanese--small, tons of brushing needed to keep from matting
Irish Water Spaniel--@ same size as boxer or lab, shedding probably about the same
Kerry Blue Terrier--@ same size as boxer, grooming required
Labradoodle--mixed breed, never know what you are gonna end up with
Lagotto Romagnolo--never heard of, no opinion
Lowchen (Little Lion Dog)--small, grooming required (daily brushing, regular groomer visits)
Maltese--too small, grooming required (daily brushing, regular groomer visits)
Malti-Poo--mixed breed, never know what you are gonna end up with
Miniature Poodle--possible good choice, need regular brushing and groomer visits for trim
Miniature Schnauzer--possible good choice, need regular brushing and groom visits for trim
Peruvian Inca Orchid--not familiar, no opinion
Polish Owczarek Nizinny--lots of brushing, probably would not play well with boxer
Poos--mixed breeds, never know what you are going to end up with
Portuguese Water Dog--same size or bigger than boxer, regular grooming required
Puli (Pulik)--only thing I know is major grooming required, whether corded or not
Schnoodle--mixed breeds, never know what you are going to end up with
Shepadoodle--mixed breeds, never know what you are going to end up with
Shichon--mixed breeds, never know what you are going to end up with
Shih-Tzu--small, grooming required (brushing and trimming)
Soft Coated Wheaten Terrier--good size, grooming required
Spanish Water Dog--not familiar with, no opinion
Standard Poodle--larger than boxer, very cool dogs though
Standard Schnauzer--could be larger than boxer, could be same size, regular grooming visits
Tibetan Terrier--needs brushed every couple days
Toy Poodle--too small to play with boxer
West Highland White Terrier--could be good choice, consider terrier attitude, grooming req.
Wirehaired Fox Terrier--could be good choice, consider terrier attitude, grooming required
Xoloitzcuintle--not familiar with, no opinion
Yorkshire Terrier--too small to play with boxer
I agree with TwoDogs, to stay away from the herding breeds. Also, not all maltese are yappy, but that is WAY too small of dog to play with a boxer. As far as "small dog syndrome", you can't have something really small and have a boxer unless they are ALWAYS totally supervised. And the barking, yapping, and nipping is an individual dog thing that you are only going to be able to control if you get the 2nd dog as a pup and do a lot of training or get the 2nd dog as an adult and know it's behavior around bigger dogs/people/experiences. As far as the pomeranians go.....I have worked for a pom breeder for all my grooming experience (she has @30 poms now) and VERY few of hers behave in the way you speak of your uncle's behaving.
I, too, have heard all the male/female talk and I don't know if it is because our girls are sisters.......but, my female boxer plays wonderfully with the female Rottie next door......so not so sure how much of that is the female/female thing and how much is reliant on the individual dog.
Even after you get a new puppy, whatever the breed, it will need to be confined when you are not there, just as your boxer was. Just because there is an "adult" dog to "teach" it, doesn't mean that a baby can hold it's bladder, not chew stuff, etc. like your adult. My girl was over 1 yr old when she wasn't getting me up in the middle of the night to go potty.
Best of luck to you whatever you choose..........and sorry this was so long, but really just trying to help you make the best decision.