Unsure how you could accomplish unaugmented/small arms melee combat without RPG rules though.
You could construct infantry squads with one member and each armed with one knife but that would most likely end with both combatants dying (using normal Battletech rules) in the first round.
Dying of boredom in the 100th turn, maybe...
A knife at the BT scale has a damage rating of 0.02; you'd need 25 troopers armed with knives to be able to even hope of doing a point of damage at that scale; even if the attack hits, you'd need to roll 11+ on the cluster hits table in order to actually deliver that one point of damage... and the loss of a single trooper makes it impossible to deal any damage at all. Since a single-trooper, single-squad platoon can take 1 point of damage, there is no way to kill it.
(Given that combatants are Elementals, the knife could represent fists as those lack rules in non-RPG environment.)
A better alternative might be the Club (Blackjack/Sap), which is a non-penetrating, point blank weapon that can deliver 0.05 points of damage; you'd need 10 troopers do deliver 1 point of damage... on a cluster hits roll of 11+
The other problem with trying to simulate personal combat at the BT "mech-scale" board is that initiative/damage resolution means that all damage is simultaneous.
It
can be done, however;
1) create two single-trooper "platoons". Each trooper armed with a "Sap" (0.05) damage, and wearing "summer clothes" (divisor 0.5 armor; effectively doubling damage received).
2) establish a threshold; "first blood", "three hits", "submission", "death", or any mutually agreed total.
3) conduct combat normally: each side rolls initiative, declares attacks, resolves the attack (i.e. "rolls to-hit"), and assigns damage, without rounding the damage received or checking cluster hits: each hit deals 0.1 points of damage.
"First Blood" = first one to hit the other wins. if both hit "first" (i.e. both hit in the first turn), either declare a draw, or continue the fight until one hits and the other one doesn't.
"Three Hits" = What it says on the tin: first one to hit the opponent three times wins.
"Submission" = Five hits are required, representing the 0.5 threshold where one normally rounds up to 1; the opponent either yielded, got knocked out/silly, or his companions intervened by "throwing in the towel"; in either case, the opponent either survives (or an infantry survival check is done).
"Death" = Ten hits are needed; the loser dies, does not pass Go and does not collect 200 C-bills.
Just an idea, of course.