Now, I know there is not a Templar alive that would deny that the Black Sword is a... sword
.
Also, it's a Power Weapon with its own special rules (S+2), so it doesn't use the "Power Weapons are what they look like" rules.
Can we say that the power weapons of the bike squadrons are lances?
If they look like lances - sure.
And can we claim that our Techmarines have Power axes? (They look like axes to me).
If it looks like an axe, and isn't specified anywhere as being a Thunderhammer, sure.
Could we do the same in any case we could convert our models to look accordingly?
Sure, so long as the model is armed with "a Power Weapon", you can convert your minis any way you want and claim the benefit based on the apparent sub-type of Power Weapon with the appropriate benefits. Just remember, if any model is armed with a "Power Weapon" which also has special rules - these override the generic Power Weapons visible sub-type rules and goes to the "Special Power Weapon are AP3 plus it's listed Special Rules" rule.
I love Tau in CC, it's like clubbing baby seals, only tau are neither cute nor fluffy or protected by the Maritime Mammal Act..... so it's perfectly legal and the Sierra Club ASPCA nuts won't come looking for you!
For the regular Guardsman you've got Commissars holding guns to their backs. They're faithful in their own way, sometimes mightily so, but they are regular folks who've led regular lives, with the completely understandable desire to continue living that causes them to duck when they get shot at. Sisters are orphans raised in perpetual Sunday school, fanatical to the point that they look at Repentia and feel a twinge of jealousy that those girls will see the Emperor sooner than they will.