is a melee only party viable?

[Stworca]

So, basically, my question is: will this party have a chance to make it trough SoA + ToB on Insane

Yes.

and what will be the most challenging fights?

Draconis, unless you get Sarevok, because he'll just proc Deathbringer through all protection spells and win you the fight.

What would be the best tactic?

Without spellcasters you can easily win fights with gear-cheese. Mace of Disruption +2 killing Kangaxx in one hit is a good example.
Cloak of shapeshifting into a jelly is a perfect tanking item for time-stops (-90% damage taken i believe)
You can also use tricks like : Slow the enemy with FoA and change everyone's weapon to ranged..

The most important thing to remember is - get ALL the boots of speed. Incl the ones from Renal. Faster moving warrior is a living one.

Edit : Ah, you've done it already. Good job.