That form of the Eastern Cross is called the “St Olha Cross.” If you wish to wear it, there is no impediment at all. You should have it blessed by a priest. In the Eastern Church, such neck Crosses are often placed on the “tetrapod” before the iconostasis for the duration of an entire Divine Liturgy before it is specially blessed by the priest.
The tradition is that one wear it on a chain or cord that is long enough to allow one to bless oneself with the Cross morning and evening (like Catholics use the Crucifix of the Rosary to bless themselves). As far as is practical, it should never be taken off, even when bathing.
There was even a church canon long ago that said that all depictions of the Cross of our Lord had to have the Christogram or the IC XC on it to signify that it was the Lord’s Cross etc. So this is the most canonical form of the neck Cross possible.
The explanation given here about the slanted foot-rest is OK, but it is a popular one, not a liturgical one.
We find the liturgical explanation in the Lenten Ninth Hour of the Byzantine daily office where the Cross is likened to a “weigh scale” where Grace outweighs our sins - thus the foot-rest comes up on our Lord’s right side. Of course, we pray that we may be brought up with the Good Thief etc.
Also, when we reverence the three Bar Cross, we always kiss the upraised point on the foot-rest and nowhere else (by tradition). On the back of this Cross are the Slavonic words for “Save and Protect.” Other Crosses have the beginning words of Psalm 67 “Let God arise . . .”
Alex