I did it by waiting until I killed Tchort to finish that quest, so all the hard work was done as a regular character. Then I did the quest, inhaled some mutagen gas, and took a train out to North Underrail.
That's the easy way. The hard way would be to become a mutant as early as possible and complete a full playthrough. You'd be dominating Underrail hardcore if you could actually do that. I don't even know if some of the plot-critical characters like Six would let you talk to them.
Here's your stats as a mutant:
Strength: 22
Dexterity: 7
Agility: 3
Constitution: 12
Perception: 3
Will: 5
Intelligence: 2
You also get 70 melee skill.
Since you're forced to use melee, maybe you could pick up some melee feats and skills? You might want these skills:
Melee: I think you get 70 free melee skill, but I don't know how it interacts with levelups.
Biology to craft more health potions, since you'll be guzzling dozens of them down and vendors will likely all attack you on sight.
Stealth, Lockpicking, Hacking to avoid fighting whenever possible
Traps: To get a slight advantage picking someone off in a fight
Dodge, Evasion: Generally useful
And these might plausibly be useful:
Chemistry: I couldn't think of anything else you could possible use.
Thought Control: So you can get Locus of Control before you mutate.
