Note that your spirits are going to be completely trashed if it ever comes to Spirit vs. Spirit combat, or astral combat of any sort for them -- since, after all, they do not have edged weapons with which to fight.
Incorrect. On the physical, the spirit would be at no more a disadvantage than any other possession spirit. As long as the vessel (which is often the swordmage himself) has a blade, or can get one, then the spirit has a blade for use on the physical. If the blade is also a weapon focus, then the blades skill will work just fine on materialized spirits. On the Astral, or any other metaplane, the Blades skill is just as useless as the Unarmed Combat spell, as the skill you'd use is Astral Combat, which swordmage spirits still have.
I agree completely with Charybdis; this tradition seems custom-made for the mystic adept. While mages can cast manabolts down their blades, and adepts can power their way through any defense, a mystic adept would truly be the fusion of the mystic and martial arts you seem to be going for with this tradition.
Understand also that though you will often have mages, whether pure or mystic adept, wielding a sword, few are going to be able to fully develop the sort of focus upon both that will be necessary for them to fully combine the two; there is just too much to develop and learn with magic to gain more than moderate competency with the blade, unless you are willing to completely ignore every other skill in the book -- at which point you're going to be hurting when it comes to getting jobs and selling gear, getting around, etc. etc.
You make sacrifices for specialization, yes. Every mage has different specialties, and different levels of advancement, depending on their tradition and focus. When I've made a mage following this tradition, I tend to start only having Pistols (Light Pistols) at 1(+2), and Blades (Swords) somewhere between 3(+2) and 5(+2), with Spellcasting at 5 and Astral Combat at 3. Out of the Conjuring group, I tend to focus on Summoning, usually not getting Binding and Banishing at all, or at lower ranks. However, I will admit that, when playing a character with this tradition, I tend to use swords and spells to deal with spirit threats, instead of Banishing and Binding. And, of course, diplomacy. Spells I usually pick are Manabolt, <Element> Bolt, Ice Slick, Increase Reflexes, Heal, Energy Aura, Astral Armor, Combat Senses, Orgy, Fashion, Mist, Makeover, <Element> Wall, etc. In other words, he has options for both mana and physical ranged attacks, and then the rest of the spells he casts are either buffs to use on himself or (possibly) others, battlefield control, and healing. Fashion and Makeover are included both as a way to become instantly prepared for a meet, whether it is in the Barrens or Dante's, and as an efficient way to change one's appearance in order to throw off pursuit, though some of the material from Attitude makes them redundant.
So he isn't likely to get a job banishing spirits, or the like, but that is already a job that tends to draw other specialists. Most combat mages tend to be, well, combat focused, afterall, which is why I said that the tradition may appeal mostly to them, rather than, say, the occult investigator or the street shaman. When you're starting out, you can either be a specialist, and fill in the gaps later, or a generalist, and build into a specialty. Depends on your focus, just like the difference between riggers and hackers.
If you really want to be the swordmage without being a Mystic Adept, invest in making some of your blades sustaining foci.
I already do this. A force 2 Weapon Focus and a force 3 Sustaining focus, usually. The Sustaining focus usually means he'll just cast Increase Reflexes on himself before he goes out, and sustain it through the focus unless he has reason to deactivate it.
