English counterpart to Japanese signal word, “Dokkoisho”

My best guess, and one I have heard older folks say to themselves in such circumstances:

easy does it
used especially in spoken English to advise someone to approach a task carefully and slowly.

^NOAD

While lifting yourself or an object, you might say oof, an onomatopoeic word: "Oof, it's difficult to get up from here."

After exerting yourself, whew: "Whew, that suitcase was heavy."

While trying to move, if your balance is shaky, whoa: "Whoa!" or "Whoa, I'd better be careful." This might be said as an admonition to yourself, or as acknowledgment that you do need a hand or need to hold the railing, when someone else is around. I think this is closest to the idea of telling yourself to relax and be aware.

I don't think speakers often say these to themselves without listeners present, so I'm not sure any of these are quite what you're looking for.

Dokkoisho, along with yoi-sho, wa-shoi, and sei-no all have quasi equivalents in English, albeit with regional variations.

Respectively, I'd suggest, "oomph," "one-two," "heave-ho," and "alley-oop."

Not universally used, but another possibility would be "here we go", having the sense of 'beginning a difficult undertaking'. Callithumpian's "easy does it" is probably the best verbal translation, though.