Oh. Don't worry. If you speak Polish good enough and the Russian accent is your only problem you shouldn't bother with it. In fact people from Russia, Belarus and Ukraine usually have this accent even when they speak native-like Polish. It sounds nice and softer that our own accent. Many people living in the East part of Poland and people whose families migrated after the WW2 from territories of today's Ukraine and Belarus speak with an accent very similar to Russian (though not exactly the same). We call it singing-like language. Of course you may sometimes find a xenophobic person or someone having bad opinion about Russians particularly - and your accent may provoke him to some unpleasant comments. Unfortunately such people happen in every nation. But I'm sure most people will be nice and helpful to you :)

Actually, as a native Polish speaker, I find it quite charming and melodious! The "eastern" Polish accents, e.g. from the area around Białystok and beyond Polish borders (Vilnius, Lviv) sound quite similar. But if you want to make your accent more Polish, there are a few simple tricks. Consider that all Polish vowels have exactly the same length (which gives the language a staccato rhythm), and that a vowel will sound exactly the same (and be just as audible) in a stressed syllable as well as as in an unstressed syllable. So the two "o"s in "oko" are exactly the same sound, similarly the three "a"s in "makatka" or the two "e"s in "szereg". This is very different from Russian, e.g. in "молоко". Polish "o" is also more open than Russian "o" and does not become a diphthong. Also notice that Russian speakers often pronounce "Ł" as a dark L. This was also the Polish stage pronunciation 70-80 years ago, but has since fallen into disuse. Nowadays, in standard Polish, "Ł" is pronounced exactly the same as English "W" in "well" . That should do the trick!